Stability of Viscous Contact Wave for Compressible Navier-Stokes Equations with a Large Initial Perturbation

作者：Hong Hakho^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2015, 31(1): 191-212.

DOI：10.1007/s10255-015-0460-x

• the compressible Navier-Stokes equations
• contact discontinuity
• stability
• decay rate
• large initial perturbation

The viscous contact wave for the compressible Navier-Stokes equations has recently been shown to be asymptotically stable provided that all the L-2 norms of initial perturbations, their derivatives and/or anti-derivatives are small. The main purpose of this paper is to study the asymptotic stability and convergence rate of the viscous contact wave with a large initial perturbation. For this purpose, we introduce a positive number l in the construction of a smooth approximation of the contact discontinuity for the compressible Euler equations and then we make the quantity l to be sufficiently large in order to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. This makes for us to estimate the L-2 norms of the solution and its derivative for perturbation system without assuming that L-2 norms of the anti-derivatives and the derivatives of initial perturbations are small.

• 出版日期2015