Global properties of solutions to 1D-viscous compressible barotropic fluid equations with density dependent viscosity

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 54, Issue 4, 2003, Pages 593-607

  Straškraba, Ivan ^a   Zlotnik, Alexander ^a,b  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

^b MOSCOW POWER ENGINEERING INSTITUTE   (Russian Federation)

Author keywords

Asymptotic behavior; Compressible fluid; Navier Stokes equations

Indexed keywords

EID: 0042243602     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-1009-z     Document Type: Article

References (21)

1. A. A. Amosov, A. A. Zlotnik, Global generalized solutions of the equations of the one-dimensional motion of a viscous heat-conducting gas, Soviet Math. Dokl. 38 (1989), 1-5.
2. A. A. Amosov, A. A. Zlotnik, Global solvability of a class of quasilinear systems of composite type with nonsmooth data, Diff. Equations 30 (1994), 545-558.
3. p-theory for the n-dimensional, stationary, compressible Navier-Stokes equations, and the incompressible limit for compressible fluids. The equilibrium solutions, Commun. Math. Phys. 109 (1987), 229-248.
4. R. J. DiPerna, P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547.
5. R. Erban, On the static-limit solutions to the Navier-Stokes equations of compressible flow, J. Math. Fluid Mech., submitted.
6. E. Feireisl, H. Petzeltová, On the zero-velocity-limit solutions to the Navier-Stokes equations of compressible flow, Manuscr. Math. 97 (1998), 109-116.
7. E. Feireisl, H. Petzeltová, Unconditional stability of stationary flows of compressible heat-conducting fluids driven by large external forces, J. Math. Fluid Mech. 1 (1999), 168-186.
8. A. Matsumura, T. Nishida, Periodic solutions of a viscous gas equation, Lect. Notes in Num. Appl. Anal 10 (1989), 49-82.
9. A. Matsumura, S. Yanagi, Uniform boundedness of the solutions for a one-dimensional isentropic model system of a compressible viscous gas, Commun. Math. Phys. 175 (1996), 259-274.
10. I. Straškraba, Asymptotic development of vacuums for 1-D Navier-Stokes equations of compressible flow, Nonlinear World 3 (1996), 519-535.
11. I. Straškraba, Global analysis of 1 - D Navier-Stokes equations with density dependent viscosity, In: Navier-Stokes equations and related nonlinear problems (H.Amann et al., eds.) VSP Utrecht, TEV Vilnius (1997), 371-390.
12. I. Straškraba, Large time behaviour of solutions to compressible Navier-Stokes equations, In: Navier-Stokes equations: theory and numerical methods (R.Salvi. ed.), Pitman Res. Notes in Math. Ser. 388 Longman (1998), 125-138.
13. I. Straškraba, A. Valli, Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations, Manuscr. Math. 62 (1988), 401-416.
14. I. Straškraba, A. Zlotnik, On a decay rate for 1D- viscous compressible barotropic fluid equations, J. Evol Equat. 2 (2002), 69-96.
15. A. Valli, Mathematical results for compressible flows, In: Mathematical topics in fluid mechanics, Pitman Res. Notes in Math. Ser. 274, John Wiley (1992), 193-229.
16. A. A. Zlotnik, On equations for one-dimensional motion of a viscous barotropic gas in the presence of a body force, Siberian Math. J. 33 (1992), 798-815.
17. A. A. Zlotnik, Uniform estimates and stabilization of solutions to equations of one-dimensional motion of a multicomponent barotropic mixture, Math. Notes 58 (1995), 885-889.
18. A. A. Zlotnik, On stabilization for equations of symmetric motion of a viscous barotropic gas with large mass force, Vestn. Moskov. Energ. Inst. (MPEI Bulletin) 4 (1997), No. 6, 57-69. (In Russian).
19. A. A. Zlotnik, Stabilization of solutions to three problems of a one-dimensional viscous barotropic gas flow, Doklady Mathematics 59 (1999). 239 - 43.
20. A. A. Zlotnik, Stabilization of solutions of a certain quasilinear system of equations with a weakly monotone nonlinearity, Diff. Equations 35 (1999). 1423-1428.
21. A. A. Zlotnik, Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations, Diff. Equations 36 (2000), 701-716.