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Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations
Compressible Navier-Stokes equations
1. | Lavryentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavryentyev pr. 15, Novosibirsk 630090, Russian Federation |
2. | Institut Elie Cartan, UMR 7502 (Nancy Université, CNRS, INRIA), Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-lès-Nancy, Cedex, France |
[1] |
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 & Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004 |
[2] |
Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure & Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675 |
[3] |
Jing Wang, Lining Tong. Stability of boundary layers for the inflow compressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2595-2613. doi: 10.3934/dcdsb.2012.17.2595 |
[4] |
Peixin Zhang, Jianwen Zhang, Junning Zhao. On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 1085-1103. doi: 10.3934/dcds.2016.36.1085 |
[5] |
Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609 |
[6] |
Dong Li, Xinwei Yu. On some Liouville type theorems for the compressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4719-4733. doi: 10.3934/dcds.2014.34.4719 |
[7] |
Zhilei Liang. Convergence rate of solutions to the contact discontinuity for the compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2013, 12 (5) : 1907-1926. doi: 10.3934/cpaa.2013.12.1907 |
[8] |
Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149 |
[9] |
Matthew Paddick. The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2673-2709. doi: 10.3934/dcds.2016.36.2673 |
[10] |
Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409 |
[11] |
Xulong Qin, Zheng-An Yao, Hongxing Zhao. One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries. Communications on Pure & Applied Analysis, 2008, 7 (2) : 373-381. doi: 10.3934/cpaa.2008.7.373 |
[12] |
Zilai Li, Zhenhua Guo. On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3903-3919. doi: 10.3934/dcdsb.2017201 |
[13] |
Tao Wang, Huijiang Zhao, Qingyang Zou. One-dimensional compressible Navier-Stokes equations with large density oscillation. Kinetic & Related Models, 2013, 6 (3) : 649-670. doi: 10.3934/krm.2013.6.649 |
[14] |
Yuming Qin, Lan Huang, Zhiyong Ma. Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1991-2012. doi: 10.3934/cpaa.2009.8.1991 |
[15] |
Ansgar Jüngel, Josipa-Pina Milišić. Full compressible Navier-Stokes equations for quantum fluids: Derivation and numerical solution. Kinetic & Related Models, 2011, 4 (3) : 785-807. doi: 10.3934/krm.2011.4.785 |
[16] |
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 & Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041 |
[17] |
Boris Haspot, Ewelina Zatorska. From the highly compressible Navier-Stokes equations to the porous medium equation -- rate of convergence. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3107-3123. doi: 10.3934/dcds.2016.36.3107 |
[18] |
Ping Chen, Ting Zhang. A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients. Communications on Pure & Applied Analysis, 2008, 7 (4) : 987-1016. doi: 10.3934/cpaa.2008.7.987 |
[19] |
Changjiang Zhu, Ruizhao Zi. Asymptotic behavior of solutions to 1D compressible Navier-Stokes equations with gravity and vacuum. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 1263-1283. doi: 10.3934/dcds.2011.30.1263 |
[20] |
Pavel I. Plotnikov, Jan Sokolowski. Optimal shape control of airfoil in compressible gas flow governed by Navier-Stokes equations. Evolution Equations & Control Theory, 2013, 2 (3) : 495-516. doi: 10.3934/eect.2013.2.495 |
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