# American Institute of Mathematical Sciences

October  2012, 17(7): 2595-2613. doi: 10.3934/dcdsb.2012.17.2595

## Stability of boundary layers for the inflow compressible Navier-Stokes equations

 1 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 2 Department of Mathematics, Shanghai University, Shanghai 200444, China

Received  April 2011 Revised  January 2012 Published  July 2012

In this paper, we consider the boundary layer stability of the one-dimensional isentropic compressible Navier-Stokes equations with an inflow boundary condition. We assume only one of the two characteristics to the corresponding Euler equations is negative up to some small time. We prove the existence of the boundary layers, then instead of using the skew symmetric matrix, we give a higher convergence rate of the approximate solution than the previous results by a standard energy method as long as the strength of the boundary layers is suitably small.
Citation: Jing Wang, Lining Tong. Stability of boundary layers for the inflow compressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2595-2613. doi: 10.3934/dcdsb.2012.17.2595
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##### References:
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