The 3D compressible Euler equations with damping in a bounded domain

Journal of Differential Equations

Volumn 246, Issue 2, 2009, Pages 581-596

  Pan, Ronghua ^a   Zhao, Kun ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

3D compressible Euler equations; Damping; Darcy's law; Porous medium flow

Indexed keywords

EID: 55349084017     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.06.007     Document Type: Article

References (38)

1. Alikakos N., and Rostamian R. Large time behavior of solutions of Neumann boundary value problem for the porous medium equation. Indiana Univ. Math. J. 30 (1981) 749-785
2. Aronson D.G. The porous media equations. In: Fasano A., and Primicerio M. (Eds). Nonlinear Diffusion Problem. Lecture Notes in Math. vol. 1224 (1986), Springer-Verlag, Berlin
3. Bourguignon J.P., and Brezis H. Remarks on the Euler equation. J. Funct. Anal. 15 (1975) 341-363
4. Constantin P., and Foias C. Navier-Stokes Equations. Chicago Lectures in Math. (1988), University of Chicago Press, Chicago
5. Coutand D., and Shkoller S. Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J. Amer. Math. Soc. 20 (2007) 829-930
6. Dafermos C.M. A system of hyperbolic conservation laws with frictional damping. Z. Angew. Math. Phys. 46 Special Issue (1995) 294-307
7. C.M. Dafermos, R.H. Pan, Global BV solutions for the p-system with frictional damping, Comm. Pure Appl. Math. (2008), in press
8. Ding X.X., Chen G.Q., and Luo P.Z. Convergence of the fraction step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics. Comm. Math. Phys. 121 (1989) 63-84
9. Evans L.C. Partial Differential Equations (1998), Amer. Math. Soc.
10. Hsiao L. Quasilinear Hyperbolic Systems and Dissipative Mechanisms (1998), World Scientific, Singapore
11. Hsiao L., and Liu T.P. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Comm. Math. Phys. 143 (1992) 599-605
12. Hsiao L., and Liu T.P. Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Chinese Ann. Math. Ser. B 14 (1993) 1-16
13. Hsiao L., and Luo T. Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media. J. Differential Equations 125 (1996) 329-365
14. Hsiao L., and Pan R.H. The damped p-system with boundary effects. Contemp. Math. vol. 255 (2000) 109-123
15. Hsiao L., and Pan R.H. Initial boundary value problem for the system of compressible adiabatic flow through porous media. J. Differential Equations 159 (1999) 280-305
16. Huang F.M., Marcati P., and Pan R.H. Convergence to Barenblatt solution for the compressible Euler equations with damping and vacuum. Arch. Ration. Mech. Anal. 176 (2005) 1-24
17. Huang F.M., and Pan R.H. Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum. J. Differential Equations 220 (2006) 207-233
18. Huang F.M., and Pan R.H. Convergence rate for compressible Euler equations with damping and vacuum. Arch. Ration. Mech. Anal. 166 (2003) 359-376
19. Liu T.P. Compressible flow with damping and vacuum. Japan J. Appl. Math. 13 (1996) 25-32
20. Luskin M., and Temple B. The existence of a global weak solution to the nonlinear water-hammer problem. Comm. Pure Appl. Math. 35 (1982) 697-735
21. Marcati P., and Mei M. Convergence to nonlinear diffusion waves for solutions of the initial boundary value problem to the hyperbolic conservation laws with damping. Quart. Appl. Math. 58 (2000) 763-783
22. Marcati P., and Pan R.H. On the diffusive profiles for the system of compressible adiabatic flow through porous media. SIAM J. Math. Anal. 33 (2001) 790-826
23. Matsumura A., and Nishida T. Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids. Comm. Math. Phys. 89 (1983) 445-464
24. Nishida T. Nonlinear hyperbolic equations and related topics in fluid dynamics. Publ. Math. D'Orsay (1978) 46-53
25. Nishihara K. Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping. J. Differential Equations 131 (1996) 171-188
26. p-convergence rate to nonlinear diffusion waves for p-system with damping. J. Differential Equations 161 (2000) 191-218
27. Nishihara K., and Yang T. Boundary effect on asymptotic behavior of solutions to the p-system with damping. J. Differential Equations 156 (1999) 439-458
28. Pan R.H. Boundary effects and large time behavior for the system of compressible adiabatic flow through porous media. Michigan Math. J. 49 (2001) 519-540
29. Pan R.H. Darcy's law as long time limit of adiabatic porous media flows. J. Differential Equations 220 (2006) 121-146
30. R.H. Pan, K. Zhao, Initial boundary value problem for compressible Euler equations with damping, Indiana Univ. J. Math. (2008), in press
31. Schochet S. The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit. Comm. Math. Phys. 104 (1986) 49-75
32. Sideris T.C., Thomases B., and Wang D.H. Long time behavior of solutions to the 3D compressible Euler equations with damping. Comm. Partial Differential Equations 28 (2003) 795-816
33. Vazquez J.L. The Porous Medium Equation: Mathematical Theory. Oxford Sci. Publ. (2007)
34. Wang W., and Yang T. The pointwise estimates of solutions for Euler equations with damping in multi-dimensions. J. Differential Equations 173 (2001) 410-450
35. p convergence of planar diffusion waves for 2-D Euler equations with damping. J. Differential Equations 242 1 (2007) 40-71
36. Xiao Y.L., and Xin Z.P. On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition. Comm. Pure Appl. Math. 60 7 (2007) 1027-1055
37. Zhao H.J. Convergence to strong nonlinear diffusion waves for solutions of p-system with damping. J. Differential Equations 174 (2001) 200-236
38. Zhu C.J. Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with damping. Sci. China Ser. A 46 (2003) 562-575