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Kinetic and Related Models (KRM)
 

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

Pages: 409 - 425, Volume 3, Issue 3, September 2010      doi:10.3934/krm.2010.3.409

 
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Feimin Huang - Institute of Applied Mathematics, AMSS and Hua Loo-Keng Key Laboratory of Mathematics, Academia Sinica, Beijing 100190, China (email)
Xiaoding Shi - Department of Mathematics, Graduate School of Science, Beijing University of Chemical and Technology, Beijing 100029, China (email)
Yi Wang - Institute of Applied Mathematics, AMSS and Hua Loo-Keng Key Laboratory of Mathematics, Academia Sinica, Beijing 100190, China (email)

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.

Keywords:  Navier-Stokes equations, viscous shock wave, stability, free boundary.
Mathematics Subject Classification:  Primary: 35Q30, 76D05, 76D33; Secondary: 76N15, 76D15.

Received: April 2010;      Revised: June 2010;      Available Online: July 2010.