-
Previous Article
Lower and upper bounds to the change of vorticity by transition from slip- to no-slip fluid flow
- DCDS-S Home
- This Issue
-
Next Article
A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium
Approximate solutions to a model of two-component reactive flow
1. | Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland, Poland |
2. | Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha, Czech Republic |
References:
[1] |
D. Bothe, On the Maxwell-Stefan approach to multicomponent diffusion, Progress in Nonlinear Differential Equations and their Applications, Springer, Basel, 80 (2011), 81-93.
doi: 10.1007/978-3-0348-0075-4_5. |
[2] |
D. Bresch and B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Comm. Math. Phys., 238 (2003), 211-223. |
[3] |
D. Bresch and B. Desjardins, On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models, J. Math. Pures Appl. (9), 86 (2006), 362-368.
doi: 10.1016/j.matpur.2006.06.005. |
[4] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl. (9), 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[5] |
D. Bresch, B. Desjardins and C.-K. Lin, On some compressible fluid models: Korteweg, lubrication, and shallow water systems, Comm. Partial Differential Equations, 28 (2003), 843-868.
doi: 10.1081/PDE-120020499. |
[6] |
G.-Q. Chen, D. Hoff and K. Trivisa, Global solutions to a model for exothermically reacting, compressible flows with large discontinuous initial data, Arch. Ration. Mech. Anal., 166 (2003), 321-358.
doi: 10.1007/s00205-002-0233-6. |
[7] |
D. Donatelli and K. Trivisa, A multidimensional model for the combustion of compressible fluids, Arch. Ration. Mech. Anal., 185 (2007), 379-408.
doi: 10.1007/s00205-006-0043-3. |
[8] |
E. Feireisl, On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable, Comment. Math. Univ. Carolin., 42 (2001), 83-98. |
[9] |
E. Feireisl and A. Novotný, Singular Limits in Thermodynamics of Viscous Fluids, Birkhäuser Verlag, Basel, 2009.
doi: 10.1007/978-3-7643-8843-0. |
[10] |
E. Feireisl, H. Petzeltová and K. Trivisa, Multicomponent reactive flows: Global-in-time existence for large data, Commun. Pure Appl. Anal., 7 (2008), 1017-1047.
doi: 10.3934/cpaa.2008.7.1017. |
[11] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2001. |
[12] |
V. Giovangigli, Multicomponent Flow Modeling, Birkhäuser Boston Inc., Boston, MA, 1999.
doi: 10.1007/978-1-4612-1580-6. |
[13] |
R. Klein, N. Botta, T. Schneider, C. D. Munz, S. Roller, A. Meister, L. Hoffmann and T. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics. Special issue on practical asymptotics, J. Engrg. Math., 39 (2001), 261-343.
doi: 10.1023/A:1004844002437. |
[14] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, AMS, Trans. Math. Monographs 23, Providence, 1967. |
[15] |
P.-L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 2, Compressible Models, Oxford Science Publications, Oxford, 1998. |
[16] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[17] |
A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equations, Comm. Partial Differential Equations, 32 (2007), 431-452.
doi: 10.1080/03605300600857079. |
[18] |
P. B. Mucha, M. Pokorný and E. Zatorska, Chemically reacting mixtures in terms of degenerated parabolic setting, J. Math. Phys., 54 (2013), 071501.
doi: 10.1063/1.4811564. |
[19] |
A. Novotný and I. Straškraba, Introduction to the Mathematical Theory of Compressible Flow, Oxford University Press, Oxford, 2004. |
[20] |
E. Zatorska, On the steady flow of a multicomponent, compressible, chemically reacting gas, Nonlinearity, 24 (2011), 3267-3278.
doi: 10.1088/0951-7715/24/11/013. |
[21] |
E. Zatorska, On the flow of chemically reacting gaseous mixture, J. Differential Equations, 253 (2012), 3471-3500.
doi: 10.1016/j.jde.2012.08.043. |
show all references
References:
[1] |
D. Bothe, On the Maxwell-Stefan approach to multicomponent diffusion, Progress in Nonlinear Differential Equations and their Applications, Springer, Basel, 80 (2011), 81-93.
doi: 10.1007/978-3-0348-0075-4_5. |
[2] |
D. Bresch and B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Comm. Math. Phys., 238 (2003), 211-223. |
[3] |
D. Bresch and B. Desjardins, On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models, J. Math. Pures Appl. (9), 86 (2006), 362-368.
doi: 10.1016/j.matpur.2006.06.005. |
[4] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl. (9), 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[5] |
D. Bresch, B. Desjardins and C.-K. Lin, On some compressible fluid models: Korteweg, lubrication, and shallow water systems, Comm. Partial Differential Equations, 28 (2003), 843-868.
doi: 10.1081/PDE-120020499. |
[6] |
G.-Q. Chen, D. Hoff and K. Trivisa, Global solutions to a model for exothermically reacting, compressible flows with large discontinuous initial data, Arch. Ration. Mech. Anal., 166 (2003), 321-358.
doi: 10.1007/s00205-002-0233-6. |
[7] |
D. Donatelli and K. Trivisa, A multidimensional model for the combustion of compressible fluids, Arch. Ration. Mech. Anal., 185 (2007), 379-408.
doi: 10.1007/s00205-006-0043-3. |
[8] |
E. Feireisl, On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable, Comment. Math. Univ. Carolin., 42 (2001), 83-98. |
[9] |
E. Feireisl and A. Novotný, Singular Limits in Thermodynamics of Viscous Fluids, Birkhäuser Verlag, Basel, 2009.
doi: 10.1007/978-3-7643-8843-0. |
[10] |
E. Feireisl, H. Petzeltová and K. Trivisa, Multicomponent reactive flows: Global-in-time existence for large data, Commun. Pure Appl. Anal., 7 (2008), 1017-1047.
doi: 10.3934/cpaa.2008.7.1017. |
[11] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2001. |
[12] |
V. Giovangigli, Multicomponent Flow Modeling, Birkhäuser Boston Inc., Boston, MA, 1999.
doi: 10.1007/978-1-4612-1580-6. |
[13] |
R. Klein, N. Botta, T. Schneider, C. D. Munz, S. Roller, A. Meister, L. Hoffmann and T. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics. Special issue on practical asymptotics, J. Engrg. Math., 39 (2001), 261-343.
doi: 10.1023/A:1004844002437. |
[14] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, AMS, Trans. Math. Monographs 23, Providence, 1967. |
[15] |
P.-L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 2, Compressible Models, Oxford Science Publications, Oxford, 1998. |
[16] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[17] |
A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equations, Comm. Partial Differential Equations, 32 (2007), 431-452.
doi: 10.1080/03605300600857079. |
[18] |
P. B. Mucha, M. Pokorný and E. Zatorska, Chemically reacting mixtures in terms of degenerated parabolic setting, J. Math. Phys., 54 (2013), 071501.
doi: 10.1063/1.4811564. |
[19] |
A. Novotný and I. Straškraba, Introduction to the Mathematical Theory of Compressible Flow, Oxford University Press, Oxford, 2004. |
[20] |
E. Zatorska, On the steady flow of a multicomponent, compressible, chemically reacting gas, Nonlinearity, 24 (2011), 3267-3278.
doi: 10.1088/0951-7715/24/11/013. |
[21] |
E. Zatorska, On the flow of chemically reacting gaseous mixture, J. Differential Equations, 253 (2012), 3471-3500.
doi: 10.1016/j.jde.2012.08.043. |
[1] |
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 |
[2] |
Xulong Qin, Zheng-An Yao, Hongxing Zhao. One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries. Communications on Pure and Applied Analysis, 2008, 7 (2) : 373-381. doi: 10.3934/cpaa.2008.7.373 |
[3] |
Guangwu Wang, Boling Guo. Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6141-6166. doi: 10.3934/dcdsb.2019133 |
[4] |
Jianwei Yang, Peng Cheng, Yudong Wang. Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity. Electronic Research Announcements, 2015, 22: 20-31. doi: 10.3934/era.2015.22.20 |
[5] |
Mei Wang, Zilai Li, Zhenhua Guo. Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary. Communications on Pure and Applied Analysis, 2017, 16 (1) : 1-24. doi: 10.3934/cpaa.2017001 |
[6] |
Wuming Li, Xiaojun Liu, Quansen Jiu. The decay estimates of solutions for 1D compressible flows with density-dependent viscosity coefficients. Communications on Pure and Applied Analysis, 2013, 12 (2) : 647-661. doi: 10.3934/cpaa.2013.12.647 |
[7] |
Quansen Jiu, Zhouping Xin. The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients. Kinetic and Related Models, 2008, 1 (2) : 313-330. doi: 10.3934/krm.2008.1.313 |
[8] |
Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 |
[9] |
Jishan Fan, Tohru Ozawa. A regularity criterion for 3D density-dependent MHD system with zero viscosity. Conference Publications, 2015, 2015 (special) : 395-399. doi: 10.3934/proc.2015.0395 |
[10] |
Weiping Yan. Existence of weak solutions to the three-dimensional density-dependent generalized incompressible magnetohydrodynamic flows. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1359-1385. doi: 10.3934/dcds.2015.35.1359 |
[11] |
Tian Ma, Shouhong Wang. Asymptotic structure for solutions of the Navier--Stokes equations. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 189-204. doi: 10.3934/dcds.2004.11.189 |
[12] |
Milan Pokorný, Piotr B. Mucha. 3D steady compressible Navier--Stokes equations. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 151-163. doi: 10.3934/dcdss.2008.1.151 |
[13] |
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 |
[14] |
Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients. Kinetic and Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004 |
[15] |
Ping Chen, Daoyuan Fang, Ting Zhang. Free boundary problem for compressible flows with density--dependent viscosity coefficients. Communications on Pure and Applied Analysis, 2011, 10 (2) : 459-478. doi: 10.3934/cpaa.2011.10.459 |
[16] |
Xian-Gao Liu, Jie Qing. Globally weak solutions to the flow of compressible liquid crystals system. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 757-788. doi: 10.3934/dcds.2013.33.757 |
[17] |
Lukáš Poul. Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains. Conference Publications, 2007, 2007 (Special) : 834-843. doi: 10.3934/proc.2007.2007.834 |
[18] |
Yuming Qin, T. F. Ma, M. M. Cavalcanti, D. Andrade. Exponential stability in $H^4$ for the Navier--Stokes equations of compressible and heat conductive fluid. Communications on Pure and Applied Analysis, 2005, 4 (3) : 635-664. doi: 10.3934/cpaa.2005.4.635 |
[19] |
Jiří Neustupa. A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1391-1400. doi: 10.3934/dcdss.2013.6.1391 |
[20] |
Xin Jiang, Zhikun She, Shigui Ruan. Global dynamics of a predator-prey system with density-dependent mortality and ratio-dependent functional response. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 1967-1990. doi: 10.3934/dcdsb.2020041 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]