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Global existence of weak solution to the free boundary problem for compressible Navier-Stokes
1. | Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi'an 710069, China |
2. | School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China |
References:
[1] |
Y. Cho, H. J. Choe and H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids, J. Math. Pures Appl., 83 (2004), 243-275.
doi: 10.1016/j.matpur.2003.11.004. |
[2] |
H. J. Choe and H. Kim, Strong solutions of the Navier-Stokes equations for isentropic compressible fluids, J. Differ. Eqs., 190 (2003), 504-523.
doi: 10.1016/S0022-0396(03)00015-9. |
[3] |
H. J. Choe and H. Kim, Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fluids, Math. Methods Appl., 28 (2005), 1-28.
doi: 10.1002/mma.545. |
[4] |
E. Feireisl, A. Novotny and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
doi: 10.1007/PL00000976. |
[5] |
E. Feireisl, On the motion of a viscous, compressible, and heat conducting fluid, Indiana Univ. Math. J., 53 (2004), 1705-1738.
doi: 10.1512/iumj.2004.53.2510. |
[6] |
E. Feireisl, Dynamics of Viscous Compressible Fluids, Oxford University Press, Oxford, 2004. |
[7] |
Z. H. Guo, H. L. Li and Z. P. Xin, Lagrange structure and dynamics for solutions to the spherically symmetric compressible Navier-Stokes equations, Commun. Math. Phys., 309 (2012), 371-412.
doi: 10.1007/s00220-011-1334-6. |
[8] |
D. Hoff, Global existence for 1D, compressible, isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc., 303 (1987), 169-181.
doi: 10.2307/2000785. |
[9] |
D. Hoff, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large discontinuous initial data, Indiana Univ. Math. J., 41 (1992), 1225-1302.
doi: 10.1512/iumj.1992.41.41060. |
[10] |
D. Hoff, Global existence of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data, J. Diff. Eqs., 120 (1995), 215-254.
doi: 10.1006/jdeq.1995.1111. |
[11] |
D. Hoff, Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data, Arch. Rat. Mech. Anal., 132 (1995), 1-14.
doi: 10.1007/BF00390346. |
[12] |
D. Hoff and H. K. Jenssen, Symmetric nonbarotropic flows with large data and forces, Arch. Ration. Mech. Anal., 173 (2004), 297-343.
doi: 10.1007/s00205-004-0318-5. |
[13] |
D. Hoff and D. Serre, The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow, SIAM J. Appl. Math., 51 (1991), 887-898.
doi: 10.1137/0151043. |
[14] |
X. D. Huang, J. Li and Z. P. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Comm. Pure Appl. Math., 65 (2012), 549-585.
doi: 10.1002/cpa.21382. |
[15] |
S. Jiang and P. Zhang, On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, Comm. Math. Phys., 215 (2001), 559-581.
doi: 10.1007/PL00005543. |
[16] |
H. Kong, Global Existence of Spherically Symmetric Weak Solutions to the Free Boundary Value Problem of 3D Isentropic Compressible Navier-Stokes Equations, Master thesis, Capital Normal University in Beijing, 2014. |
[17] |
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), 273-282. |
[18] |
P. L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 2. Compressible models, Oxford University Press, New York, 1998. |
[19] |
T. Luo, Z. P. Xin and T. Yang, Interface behavior of compressible Navier-Stokes equations with vacuum, SIAM J. Math. Anal., 31 (2000), 1175-1191.
doi: 10.1137/S0036141097331044. |
[20] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heatconductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[21] |
J. Nash, Le problème de Cauchy pour les équations différentielles d'un fluide général, Bull. Soc. Math. France, 90 (1962), 487-497. |
[22] |
M. Okada, Free boundary problem for the equation of one dimensional motion of viscous gas, Japan J. Appl. Math., 6 (1989), 161-177.
doi: 10.1007/BF03167921. |
[23] |
M. Okada and T. Makino, Free boundary problem for the equation of spherically Symmetrical motion of viscous gas, Japan J. Appl. Math., 10 (1993), 219-235.
doi: 10.1007/BF03167573. |
[24] |
R. Salvi and I. Straškraba, Global existence for viscous compressible fluids and their behavior as $ t\rightarrow\infty$, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 40 (1993), 17-51. |
[25] |
J. Serrin, On the uniqueness of compressible fluid motion, Arch. Rational. Mech. Anal., 3 (1959), 271-288. |
[26] |
Z. P. Xin, Blowup of smooth solutions to the compressible Navier-Stokes equations with compact density, Comm. Pure Appl. Math., 51 (1998), 229-240.
doi: 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C. |
show all references
References:
[1] |
Y. Cho, H. J. Choe and H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids, J. Math. Pures Appl., 83 (2004), 243-275.
doi: 10.1016/j.matpur.2003.11.004. |
[2] |
H. J. Choe and H. Kim, Strong solutions of the Navier-Stokes equations for isentropic compressible fluids, J. Differ. Eqs., 190 (2003), 504-523.
doi: 10.1016/S0022-0396(03)00015-9. |
[3] |
H. J. Choe and H. Kim, Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fluids, Math. Methods Appl., 28 (2005), 1-28.
doi: 10.1002/mma.545. |
[4] |
E. Feireisl, A. Novotny and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
doi: 10.1007/PL00000976. |
[5] |
E. Feireisl, On the motion of a viscous, compressible, and heat conducting fluid, Indiana Univ. Math. J., 53 (2004), 1705-1738.
doi: 10.1512/iumj.2004.53.2510. |
[6] |
E. Feireisl, Dynamics of Viscous Compressible Fluids, Oxford University Press, Oxford, 2004. |
[7] |
Z. H. Guo, H. L. Li and Z. P. Xin, Lagrange structure and dynamics for solutions to the spherically symmetric compressible Navier-Stokes equations, Commun. Math. Phys., 309 (2012), 371-412.
doi: 10.1007/s00220-011-1334-6. |
[8] |
D. Hoff, Global existence for 1D, compressible, isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc., 303 (1987), 169-181.
doi: 10.2307/2000785. |
[9] |
D. Hoff, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large discontinuous initial data, Indiana Univ. Math. J., 41 (1992), 1225-1302.
doi: 10.1512/iumj.1992.41.41060. |
[10] |
D. Hoff, Global existence of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data, J. Diff. Eqs., 120 (1995), 215-254.
doi: 10.1006/jdeq.1995.1111. |
[11] |
D. Hoff, Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data, Arch. Rat. Mech. Anal., 132 (1995), 1-14.
doi: 10.1007/BF00390346. |
[12] |
D. Hoff and H. K. Jenssen, Symmetric nonbarotropic flows with large data and forces, Arch. Ration. Mech. Anal., 173 (2004), 297-343.
doi: 10.1007/s00205-004-0318-5. |
[13] |
D. Hoff and D. Serre, The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow, SIAM J. Appl. Math., 51 (1991), 887-898.
doi: 10.1137/0151043. |
[14] |
X. D. Huang, J. Li and Z. P. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Comm. Pure Appl. Math., 65 (2012), 549-585.
doi: 10.1002/cpa.21382. |
[15] |
S. Jiang and P. Zhang, On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, Comm. Math. Phys., 215 (2001), 559-581.
doi: 10.1007/PL00005543. |
[16] |
H. Kong, Global Existence of Spherically Symmetric Weak Solutions to the Free Boundary Value Problem of 3D Isentropic Compressible Navier-Stokes Equations, Master thesis, Capital Normal University in Beijing, 2014. |
[17] |
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), 273-282. |
[18] |
P. L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 2. Compressible models, Oxford University Press, New York, 1998. |
[19] |
T. Luo, Z. P. Xin and T. Yang, Interface behavior of compressible Navier-Stokes equations with vacuum, SIAM J. Math. Anal., 31 (2000), 1175-1191.
doi: 10.1137/S0036141097331044. |
[20] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heatconductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[21] |
J. Nash, Le problème de Cauchy pour les équations différentielles d'un fluide général, Bull. Soc. Math. France, 90 (1962), 487-497. |
[22] |
M. Okada, Free boundary problem for the equation of one dimensional motion of viscous gas, Japan J. Appl. Math., 6 (1989), 161-177.
doi: 10.1007/BF03167921. |
[23] |
M. Okada and T. Makino, Free boundary problem for the equation of spherically Symmetrical motion of viscous gas, Japan J. Appl. Math., 10 (1993), 219-235.
doi: 10.1007/BF03167573. |
[24] |
R. Salvi and I. Straškraba, Global existence for viscous compressible fluids and their behavior as $ t\rightarrow\infty$, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 40 (1993), 17-51. |
[25] |
J. Serrin, On the uniqueness of compressible fluid motion, Arch. Rational. Mech. Anal., 3 (1959), 271-288. |
[26] |
Z. P. Xin, Blowup of smooth solutions to the compressible Navier-Stokes equations with compact density, Comm. Pure Appl. Math., 51 (1998), 229-240.
doi: 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C. |
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