-
Previous Article
Orbitally stable standing waves for the asymptotically linear one-dimensional NLS
- EECT Home
- This Issue
-
Next Article
Vibrations of a damped extensible beam between two stops
Sensitivity analysis for a free boundary fluid-elasticity interaction
1. | NC State University, Department of Mathematics, 3236 SAS Hall, Raleigh, NC 27695-8205 |
2. | CNRS-INLN, 1361 Routes des Lucioles, Sophia Antipolis, F-06560 Valbonne |
References:
[1] |
G. Avalos and R. Triggiani, The coupled PDE system arising in fluid/structure interaction. Part I: Explicit semigroup generator and its spectral properties, in "Fluids and Waves," Contemp. Math., 440, AMS, Providence, RI, (2007), 15-54.
doi: 10.1090/conm/440/08475. |
[2] |
V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model, in "Fluids and Waves," Contem. Math., 440, AMS, Providence, RI, (2007), 55-82.
doi: 10.1090/conm/440/08476. |
[3] |
V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Smoothness of weak solutions to a nonlinear fluid-structure interaction model, Indiana Univ. Math. J., 57 (2008), 1173-1207.
doi: 10.1512/iumj.2008.57.3284. |
[4] |
L. Bociu, Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping, Nonlinear Analysis A: Theory, Methods and Applications, 71 (2009), e560-e575.
doi: 10.1016/j.na.2008.11.062. |
[5] |
L. Bociu and I. Lasiecka, Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping, Applicationes Mathematicae, 35 (2008), 281-304.
doi: 10.4064/am35-3-3. |
[6] |
L. Bociu and I. Lasiecka, Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping, Discrete Contin. Dyn. Syst., 22 (2008), 835-860.
doi: 10.3934/dcds.2008.22.835. |
[7] |
L. Bociu and I. Lasiecka, Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping, JDE, 249 (2010), 654-683.
doi: 10.1016/j.jde.2010.03.009. |
[8] |
L. Bociu and P. Radu, Existence and uniqueness of weak solutions to the cauchy problem of a semilinear wave equation with supercritical interior source and damping, Discrete Contin. Dyn. Syst., 2009, Dynamical Systems, Differential Equations and Applications, 7th AIMS Confernece, suppl., 60-71. |
[9] |
L. Bociu and J.-P. Zolésio, Linearization of a coupled system of nonlinear elasticity and viscous fluid, in "Modern Aspects of the Theory of Partial Differential Equations," Operator Theory: Advances and Applications, 216, Birkhäuser/Springer Basel AG, Basel, (2011), 93-120.
doi: 10.1007/978-3-0348-0069-3_6. |
[10] |
L. Bociu and J.-P. Zolésio, Existence for the linearization of a steady state fluid - nonlinear elasticity interaction, Discrete and Continuous Dynamical Systems, Supplement, (2011), 184-197. |
[11] |
S. Boisgérault and J. P. Zolésio, Boundary variations in the Navier-Stokes equations and Lagrangian functionals, in "Shape Optimization and Optimal Design" (Cambridge, 1999), Lecture Notes in Pure and Appl. Math., 216, Dekker, New York, (2001), 7-26. |
[12] |
M. Boulakia, Existence of weak solutions for the three dimensional motion of an elastic structure in an incompressible fluid, J. Math. Fluid Mech., 9 (2007), 262-294.
doi: 10.1007/s00021-005-0201-7. |
[13] |
S. Čanić, A. Mikelić, T.-B. Kim and G. Guidoboni, Existence of a unique solution to a nonlinear moving-boundary problem of mixed type arising in modeling blood flow, in "Nonlinear Conservation Laws and Applications," IMA Vol. Math. Appl., 153, Springer, New York, (2011), 235-256.
doi: 10.1007/978-1-4419-9554-4_11. |
[14] |
P. G. Ciarlet, "Mathematical Elasticity. Volume I: Three-dimensional Elasticity," Studies in Mathematics and its Applications, 20, North-Holland Publishing Co., Amsterdam, 1988. |
[15] |
C. Conca, J. San Martin and M. Tucsnak, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations, 25 (2000), 1019-1042.
doi: 10.1080/03605300008821540. |
[16] |
D. Coutand and S. Shkoller, Motion of an elastic solid inside and incompressible viscous fluid, Arch. Rational Mech. Anal., 176 (2005), 25-102.
doi: 10.1007/s00205-004-0340-7. |
[17] |
D. Coutand and S. Shkoller, The interaction between quasilinear elastodynamics and the Navier-Stokes equations, Arch. Rational Mech. Anal. 179 (2006), 303-352.
doi: 10.1007/s00205-005-0385-2. |
[18] |
M. C. Delfour and J.-P. Zolésio, "Shapes and Geometries. Analysis, Differential Calculus and Optimization," Advances in Design and Control, 4, SIAM, Philadelphia, PA, 2001. |
[19] |
M. C. Delfour and J.-P. Zolésio, Hidden boundary smoothness for some classes of differential equations on submanifolds, in " Optimization Methods in Partial Differential Equations" (South Hadley, MA, 1996), Contemporary Mathematics, 209, AMS, Providence, RI, (1997), 59-73.
doi: 10.1090/conm/209/02759. |
[20] |
F. R. Desaint and J.-P. Zolésio, Manifold derivative in the Laplace-Beltrami equation, J. Funct. Anal., 151 (1997), 234-269.
doi: 10.1006/jfan.1997.3130. |
[21] |
B. Desjardins, M. J. Esteban, C. Grandmont and P. Le Tallec, Weak solutions for a fluid-elastic structure interaction model, Rev. Math. Complut., 14 (2001), 523-538. |
[22] |
B. Desjardins and M. J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Ration. Mech. Anal., 146 (1999), 59-71.
doi: 10.1007/s002050050136. |
[23] |
Q. Du, M. D. Gunzburger, L. S. Hou and J. Lee, Analysis of a linear fluid-structure interaction problem, DCDS, 9 (2003), 633-650.
doi: 10.3934/dcds.2003.9.633. |
[24] |
R. Dziri and J.-P. Zolésio, Dynamical shape control in non-cylindrical Navier-Stokes equations, J. Convex Anal., 6 (1999), 293-318. |
[25] |
E. Feireisl, On the motion of rigid bodies in a viscous incompressible fluid, J. Evol. Equations, 3 (2003), 419-441.
doi: 10.1007/s00028-003-0110-1. |
[26] |
L. Formaggia, A. Quarteroni and A. Veneziani, eds., "Cardiovascular Mathematics. Modeling and Simulation of the Circulatory System," MS&A, Modeling, Simulation and Applications, 1, Springer-Verlag Italia, Milano, 2009.
doi: 10.1007/978-88-470-1152-6. |
[27] |
C. Grandmont and Y. Maday, Existence for unsteady fluid-structure interaction problem, M2AN Math. Model. Numer. Anal., 34 (2000), 609-636.
doi: 10.1051/m2an:2000159. |
[28] |
M. D. Gunzburger, H.-C. Lee and G. A. Seregin, Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions, J. Math. Fluid Mech., 2 (2000), 219-266.
doi: 10.1007/PL00000954. |
[29] |
E. Kaya, E. Aulisa, A. Ibragimov and P. Seshaiyer, A stability estimate for fluid structure interaction problem with non-linear beam, DCDS-S, 2009, Dynamical Systems, Differential Equations and Applications, 7th AIMS Conference, suppl., 424-432. |
[30] |
T. Kim, S. Čanić and G. Guidoboni, Existence and uniqueness of a solution to a three-dimensional axially symmetric biot problem arising in modeling blood flow, Communications on Pure and Applied Analysis, 9 (2010), 839-865.
doi: 10.3934/cpaa.2010.9.839. |
[31] |
I. Kukavica, A. Tuffaha and M. Ziane, Strong solutions to a nonlinear fluid structure interaction system, J. Diff. Eq., 247 (2009), 1452-1478.
doi: 10.1016/j.jde.2009.06.005. |
[32] |
I. Kukavica, A. Tuffaha and M. Ziane, Strong solutions to a Navier-Stokes-Lamé system on a domain with a non-flat boundary, Nonlinearity, 24 (2011), 159-176.
doi: 10.1088/0951-7715/24/1/008. |
[33] |
I. Lasiecka and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theories," Volumes I and II, Cambridge, University Press, 2000. |
[34] |
I.Lasiecka and A. Tuffaha, Optimal feedback synthesis for bolza control problem arising in linearized fluid structure interaction, in " Optimal Control of Coupled Systems of Partial Differential Equations," International Series of Numerical Mathematics, 158, Birkhäuser Verlag, Basel, (2009), 171-190.
doi: 10.1007/978-3-7643-8923-9_10. |
[35] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problemes aux Limites Non Linéaires," Dunod, 1969. |
[36] |
P. I. Plotnikov and J. Sokolowski, Shape derivative of drag functional, SIAM J. Control Optim., 48 (2010), 4680-4706.
doi: 10.1137/090758179. |
[37] |
J. A. San Martin, V. Starovoitov and M. Tucsnak, Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Ration. Mech. Anal., 161 (2002), 113-147.
doi: 10.1007/s002050100172. |
[38] |
J. Sokolowski and J.-P. Zolésio, "Introduction to Shape Optimization. Shape Sensitivity Analysis," Springer Series in Computational Mathematics, 16, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58106-9. |
[39] |
B. N. Steele, D. Valdez-Jasso, M. A. Haider and M. S. Olufsen, Predicting arterial flow and pressure dynamics using a 1D fluid dynamics model with a viscoelastic wall, SIAM J. Appl. Math., 71 (2011), 1123-1143.
doi: 10.1137/100810186. |
[40] |
D. Tataru, On the regularity of boundary traces for the wave equation, Annali di Scuola Normale Sup. Pisa Cl. Sci. (4), 26 (1998), 185-206. |
[41] |
J.-P. Zolésio, Weak shape formulation of free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 21 (1994), 11-44. |
show all references
References:
[1] |
G. Avalos and R. Triggiani, The coupled PDE system arising in fluid/structure interaction. Part I: Explicit semigroup generator and its spectral properties, in "Fluids and Waves," Contemp. Math., 440, AMS, Providence, RI, (2007), 15-54.
doi: 10.1090/conm/440/08475. |
[2] |
V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model, in "Fluids and Waves," Contem. Math., 440, AMS, Providence, RI, (2007), 55-82.
doi: 10.1090/conm/440/08476. |
[3] |
V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Smoothness of weak solutions to a nonlinear fluid-structure interaction model, Indiana Univ. Math. J., 57 (2008), 1173-1207.
doi: 10.1512/iumj.2008.57.3284. |
[4] |
L. Bociu, Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping, Nonlinear Analysis A: Theory, Methods and Applications, 71 (2009), e560-e575.
doi: 10.1016/j.na.2008.11.062. |
[5] |
L. Bociu and I. Lasiecka, Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping, Applicationes Mathematicae, 35 (2008), 281-304.
doi: 10.4064/am35-3-3. |
[6] |
L. Bociu and I. Lasiecka, Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping, Discrete Contin. Dyn. Syst., 22 (2008), 835-860.
doi: 10.3934/dcds.2008.22.835. |
[7] |
L. Bociu and I. Lasiecka, Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping, JDE, 249 (2010), 654-683.
doi: 10.1016/j.jde.2010.03.009. |
[8] |
L. Bociu and P. Radu, Existence and uniqueness of weak solutions to the cauchy problem of a semilinear wave equation with supercritical interior source and damping, Discrete Contin. Dyn. Syst., 2009, Dynamical Systems, Differential Equations and Applications, 7th AIMS Confernece, suppl., 60-71. |
[9] |
L. Bociu and J.-P. Zolésio, Linearization of a coupled system of nonlinear elasticity and viscous fluid, in "Modern Aspects of the Theory of Partial Differential Equations," Operator Theory: Advances and Applications, 216, Birkhäuser/Springer Basel AG, Basel, (2011), 93-120.
doi: 10.1007/978-3-0348-0069-3_6. |
[10] |
L. Bociu and J.-P. Zolésio, Existence for the linearization of a steady state fluid - nonlinear elasticity interaction, Discrete and Continuous Dynamical Systems, Supplement, (2011), 184-197. |
[11] |
S. Boisgérault and J. P. Zolésio, Boundary variations in the Navier-Stokes equations and Lagrangian functionals, in "Shape Optimization and Optimal Design" (Cambridge, 1999), Lecture Notes in Pure and Appl. Math., 216, Dekker, New York, (2001), 7-26. |
[12] |
M. Boulakia, Existence of weak solutions for the three dimensional motion of an elastic structure in an incompressible fluid, J. Math. Fluid Mech., 9 (2007), 262-294.
doi: 10.1007/s00021-005-0201-7. |
[13] |
S. Čanić, A. Mikelić, T.-B. Kim and G. Guidoboni, Existence of a unique solution to a nonlinear moving-boundary problem of mixed type arising in modeling blood flow, in "Nonlinear Conservation Laws and Applications," IMA Vol. Math. Appl., 153, Springer, New York, (2011), 235-256.
doi: 10.1007/978-1-4419-9554-4_11. |
[14] |
P. G. Ciarlet, "Mathematical Elasticity. Volume I: Three-dimensional Elasticity," Studies in Mathematics and its Applications, 20, North-Holland Publishing Co., Amsterdam, 1988. |
[15] |
C. Conca, J. San Martin and M. Tucsnak, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations, 25 (2000), 1019-1042.
doi: 10.1080/03605300008821540. |
[16] |
D. Coutand and S. Shkoller, Motion of an elastic solid inside and incompressible viscous fluid, Arch. Rational Mech. Anal., 176 (2005), 25-102.
doi: 10.1007/s00205-004-0340-7. |
[17] |
D. Coutand and S. Shkoller, The interaction between quasilinear elastodynamics and the Navier-Stokes equations, Arch. Rational Mech. Anal. 179 (2006), 303-352.
doi: 10.1007/s00205-005-0385-2. |
[18] |
M. C. Delfour and J.-P. Zolésio, "Shapes and Geometries. Analysis, Differential Calculus and Optimization," Advances in Design and Control, 4, SIAM, Philadelphia, PA, 2001. |
[19] |
M. C. Delfour and J.-P. Zolésio, Hidden boundary smoothness for some classes of differential equations on submanifolds, in " Optimization Methods in Partial Differential Equations" (South Hadley, MA, 1996), Contemporary Mathematics, 209, AMS, Providence, RI, (1997), 59-73.
doi: 10.1090/conm/209/02759. |
[20] |
F. R. Desaint and J.-P. Zolésio, Manifold derivative in the Laplace-Beltrami equation, J. Funct. Anal., 151 (1997), 234-269.
doi: 10.1006/jfan.1997.3130. |
[21] |
B. Desjardins, M. J. Esteban, C. Grandmont and P. Le Tallec, Weak solutions for a fluid-elastic structure interaction model, Rev. Math. Complut., 14 (2001), 523-538. |
[22] |
B. Desjardins and M. J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Ration. Mech. Anal., 146 (1999), 59-71.
doi: 10.1007/s002050050136. |
[23] |
Q. Du, M. D. Gunzburger, L. S. Hou and J. Lee, Analysis of a linear fluid-structure interaction problem, DCDS, 9 (2003), 633-650.
doi: 10.3934/dcds.2003.9.633. |
[24] |
R. Dziri and J.-P. Zolésio, Dynamical shape control in non-cylindrical Navier-Stokes equations, J. Convex Anal., 6 (1999), 293-318. |
[25] |
E. Feireisl, On the motion of rigid bodies in a viscous incompressible fluid, J. Evol. Equations, 3 (2003), 419-441.
doi: 10.1007/s00028-003-0110-1. |
[26] |
L. Formaggia, A. Quarteroni and A. Veneziani, eds., "Cardiovascular Mathematics. Modeling and Simulation of the Circulatory System," MS&A, Modeling, Simulation and Applications, 1, Springer-Verlag Italia, Milano, 2009.
doi: 10.1007/978-88-470-1152-6. |
[27] |
C. Grandmont and Y. Maday, Existence for unsteady fluid-structure interaction problem, M2AN Math. Model. Numer. Anal., 34 (2000), 609-636.
doi: 10.1051/m2an:2000159. |
[28] |
M. D. Gunzburger, H.-C. Lee and G. A. Seregin, Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions, J. Math. Fluid Mech., 2 (2000), 219-266.
doi: 10.1007/PL00000954. |
[29] |
E. Kaya, E. Aulisa, A. Ibragimov and P. Seshaiyer, A stability estimate for fluid structure interaction problem with non-linear beam, DCDS-S, 2009, Dynamical Systems, Differential Equations and Applications, 7th AIMS Conference, suppl., 424-432. |
[30] |
T. Kim, S. Čanić and G. Guidoboni, Existence and uniqueness of a solution to a three-dimensional axially symmetric biot problem arising in modeling blood flow, Communications on Pure and Applied Analysis, 9 (2010), 839-865.
doi: 10.3934/cpaa.2010.9.839. |
[31] |
I. Kukavica, A. Tuffaha and M. Ziane, Strong solutions to a nonlinear fluid structure interaction system, J. Diff. Eq., 247 (2009), 1452-1478.
doi: 10.1016/j.jde.2009.06.005. |
[32] |
I. Kukavica, A. Tuffaha and M. Ziane, Strong solutions to a Navier-Stokes-Lamé system on a domain with a non-flat boundary, Nonlinearity, 24 (2011), 159-176.
doi: 10.1088/0951-7715/24/1/008. |
[33] |
I. Lasiecka and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theories," Volumes I and II, Cambridge, University Press, 2000. |
[34] |
I.Lasiecka and A. Tuffaha, Optimal feedback synthesis for bolza control problem arising in linearized fluid structure interaction, in " Optimal Control of Coupled Systems of Partial Differential Equations," International Series of Numerical Mathematics, 158, Birkhäuser Verlag, Basel, (2009), 171-190.
doi: 10.1007/978-3-7643-8923-9_10. |
[35] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problemes aux Limites Non Linéaires," Dunod, 1969. |
[36] |
P. I. Plotnikov and J. Sokolowski, Shape derivative of drag functional, SIAM J. Control Optim., 48 (2010), 4680-4706.
doi: 10.1137/090758179. |
[37] |
J. A. San Martin, V. Starovoitov and M. Tucsnak, Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Ration. Mech. Anal., 161 (2002), 113-147.
doi: 10.1007/s002050100172. |
[38] |
J. Sokolowski and J.-P. Zolésio, "Introduction to Shape Optimization. Shape Sensitivity Analysis," Springer Series in Computational Mathematics, 16, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-642-58106-9. |
[39] |
B. N. Steele, D. Valdez-Jasso, M. A. Haider and M. S. Olufsen, Predicting arterial flow and pressure dynamics using a 1D fluid dynamics model with a viscoelastic wall, SIAM J. Appl. Math., 71 (2011), 1123-1143.
doi: 10.1137/100810186. |
[40] |
D. Tataru, On the regularity of boundary traces for the wave equation, Annali di Scuola Normale Sup. Pisa Cl. Sci. (4), 26 (1998), 185-206. |
[41] |
J.-P. Zolésio, Weak shape formulation of free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 21 (1994), 11-44. |
[1] |
Hantaek Bae. Solvability of the free boundary value problem of the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 769-801. doi: 10.3934/dcds.2011.29.769 |
[2] |
Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic and Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409 |
[3] |
Zilai Li, Zhenhua Guo. On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3903-3919. doi: 10.3934/dcdsb.2017201 |
[4] |
Xulong Qin, Zheng-An Yao. Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041 |
[5] |
Zhenhua Guo, Zilai Li. Global existence of weak solution to the free boundary problem for compressible Navier-Stokes. Kinetic and Related Models, 2016, 9 (1) : 75-103. doi: 10.3934/krm.2016.9.75 |
[6] |
Yoshihiro Shibata. On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1681-1721. doi: 10.3934/cpaa.2018081 |
[7] |
Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1185-1196. doi: 10.3934/dcds.2010.26.1185 |
[8] |
Vena Pearl Bongolan-walsh, David Cheban, Jinqiao Duan. Recurrent motions in the nonautonomous Navier-Stokes system. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 255-262. doi: 10.3934/dcdsb.2003.3.255 |
[9] |
A. V. Fursikov. Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 289-314. doi: 10.3934/dcds.2004.10.289 |
[10] |
Donatella Donatelli, Eduard Feireisl, Antonín Novotný. On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 783-798. doi: 10.3934/dcdsb.2010.13.783 |
[11] |
Wenjing Song, Ganshan Yang. The regularization of solution for the coupled Navier-Stokes and Maxwell equations. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2113-2127. doi: 10.3934/dcdss.2016087 |
[12] |
Jie Liao, Xiao-Ping Wang. Stability of an efficient Navier-Stokes solver with Navier boundary condition. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 153-171. doi: 10.3934/dcdsb.2012.17.153 |
[13] |
Yoshikazu Giga. A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1277-1289. doi: 10.3934/dcdss.2013.6.1277 |
[14] |
Pavel I. Plotnikov, Jan Sokolowski. Optimal shape control of airfoil in compressible gas flow governed by Navier-Stokes equations. Evolution Equations and Control Theory, 2013, 2 (3) : 495-516. doi: 10.3934/eect.2013.2.495 |
[15] |
Hongjie Dong, Kunrui Wang. Interior and boundary regularity for the Navier-Stokes equations in the critical Lebesgue spaces. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5289-5323. doi: 10.3934/dcds.2020228 |
[16] |
Jing Wang, Lining Tong. Stability of boundary layers for the inflow compressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2595-2613. doi: 10.3934/dcdsb.2012.17.2595 |
[17] |
Chérif Amrouche, Nour El Houda Seloula. $L^p$-theory for the Navier-Stokes equations with pressure boundary conditions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1113-1137. doi: 10.3934/dcdss.2013.6.1113 |
[18] |
Sylvie Monniaux. Various boundary conditions for Navier-Stokes equations in bounded Lipschitz domains. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1355-1369. doi: 10.3934/dcdss.2013.6.1355 |
[19] |
Platon Surkov. Dynamical estimation of a noisy input in a system with a Caputo fractional derivative. The case of continuous measurements of a part of phase coordinates. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022020 |
[20] |
Lorena Bociu, Jean-Paul Zolésio. Existence for the linearization of a steady state fluid/nonlinear elasticity interaction. Conference Publications, 2011, 2011 (Special) : 184-197. doi: 10.3934/proc.2011.2011.184 |
2021 Impact Factor: 1.169
Tools
Metrics
Other articles
by authors
[Back to Top]