Stability of viscous shock wave for compressibleNavier-Stokes equations with free boundary

Feimin Huang; Xiaoding Shi; Yi Wang

doi:10.3934/krm.2010.3.409

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2010, Volume 3, Issue 3: 409-425. Doi: 10.3934/krm.2010.3.409

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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
2.
Department of Mathematics, Graduate School of Science, Beijing University of Chemical and Technology, Beijing 100029

Received: April 2010

Revised: June 2010

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q30, 76D05, 76D33; Secondary: 76N15, 76D15.

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

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