# American Institute of Mathematical Sciences

September  2010, 3(3): 409-425. doi: 10.3934/krm.2010.3.409

## Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary

 1 Institute of Applied Mathematics, AMSS and Hua Loo-Keng Key Laboratory of Mathematics, Academia Sinica, Beijing 100190, China, China 2 Department of Mathematics, Graduate School of Science, Beijing University of Chemical and Technology, Beijing 100029, China

Received  April 2010 Revised  June 2010 Published  July 2010

A free boundary problem for the one-dimensional compressible Navier-Stokes equations in Eulerian coordinate is investigated. The stability of the viscous shock wave to the free boundary problem is established under some smallness conditions. The proof is given by an elementary energy method.
Citation: Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409
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