Interior regularity of the compressibleNavier-Stokes equations  with degenerate  viscosity  coefficient andvacuum

Yuming Qin; Lan Huang; Shuxian Deng; Zhiyong Ma; Xiaoke Su; Xinguang Yang

doi:10.3934/dcdss.2009.2.163

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2009, Volume 2, Issue 1: 163-192. Doi: 10.3934/dcdss.2009.2.163

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Interior regularity of the compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum

1.
Department of Mathematics - Henan University,Kaifeng 475001
2.
College of Information Science and Technology, Donghua University, Shanghai 201620

Received: July 2008

Revised: November 2008

Published: March 2009

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Abstract

This paper is concerned with the interior regularity of global solutions for the one-dimensional compressible isentropic Navier-Stokes equations with degenerate viscosity coefficient and vacuum. The viscosity coefficient $\mu$ is proportional to $\rho^{\theta}$ with $0<\theta<1/3$, where $\rho$ is the density. The global existence has been established in [44] (Vong, Yang and Zhu, J. Differential Equations, 192(2), 475--501). Some ideas and more delicate estimates are introduced to prove these results.

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Mathematics Subject Classification: Primary: 35Q30, 35D10; Secondary: 76N10.

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Interior regularity of the compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum

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