Asymptotic Stability of the Stationary Solution to the Compressible Navier-Stokes Equations in the Half Space

Communications in Mathematical Physics

Volumn 240, Issue 3, 2003, Pages 483-500

  Kawashima, Shuichi ^a   Nishibata, Shinya ^b   Zhu, Peicheng ^a  

^a KYUSHU UNIVERSITY   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141792302     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0909-2     Document Type: Article

References (13)

1. Friedman, A.: Partial Differential Equations of Parabolic Type. Englewood Cliffs, NJ: Prentice Hall, Inc., 1964
2. Il'in, A., Oleinik, O.: Asymptotic behavior of the solutions of Cauchy problems for certain quasilinear equations for large time (Russian). Mat. Sb. 51, 191-216 (1960)
3. Kawashima, S., Nishibata, S.: Stationary waves for the discrete Boltzmann equation in the half space with the reflective boundaries. Commun. Math. Phys. 211, 183-206 (2000)
4. Kawashima, S., Nishida, T.: Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gases. J. Math. Kyoto Univ. 21(4), 825-837 (1981)
5. Kawashima, S., Zhu, P.: Asymptotic stability of the rarefaction waves of compressible Navier-Stokes equations in the half space. To appear
6. Kawashima, S., Zhu, P.: Asymptotic stability of the superposition of nonlinear waves of compressible Navier-Stokes equations in the half space. To appear
7. Liu, T., Matsumura, A., Nishihara, K.: Behaviors of solutions for the Burgers equations with boundary corresponding to rarefaction waves. SIAM J. Math. Anal. 29, 293-308 (1998)
8. Liu, T., Nishihara, K.: Asymptotic behavior for scalar viscous conservation laws with boundary effect. J. Diff. Eq. 133, 296-320 (1997)
9. Matsumura, A.: Inflow and outflow problems in the half space for a one-dimensional isentropic model system for compressible viscous gas. In: Proceedings of IMS Conference on Differential Equations from Mechanics. Hong Kong, 1999
10. Matsumura, A., Mei, M.: Asymptotics toward viscous shock profile for solution of the viscous p-System with boundary effect. Arch. Rat. Mech. Anal. 146, 1-22 (1999)
11. Matsumura, A., Nishihara, K.: Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional isentropic model system for compressible viscous gas. Commun. Math. Phys. 222, 449-474 (2001)
12. Nishibata, S.: Asymptotic stability of traveling waves to a certain discrete velocity model of the Boltzmann equation in the half space. SIAM J. Math. Anal. 34, 555-572 (2002)
13. Nikkuni, Y., Kawashima, S.: Stability of stationary solutions to the half-space problem for the discrete Boltzmann equation with multiple collisions. Kyushu J. Math. 54, 233-255 (2000)