Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equations. (English) Zbl 1065.35057
The one-dimensional compressible Navier-Stokes equations in Lagrangian coordinates are considered. The time-asymptotic behaviour of strong rarefaction waves of solutions of the considered problem is studied. The authors prove a local stability result for a general gas. Then, a global stability result for the ideal polytropic gas is obtained. A global stability result for a general isentropic gas is also established.
Reviewer: Ruxandra Stavre (Bucureşti)
MSC:
35B35 | Stability in context of PDEs |
35L65 | Hyperbolic conservation laws |
35L60 | First-order nonlinear hyperbolic equations |
35Q35 | PDEs in connection with fluid mechanics |
76N99 | Compressible fluids and gas dynamics |