On the Stokes approximation equations for two-dimensional compressible flows

Qing Yi

doi:10.3934/krm.2013.6.205

Article Contents

2013, Volume 6, Issue 1: 205-218. Doi: 10.3934/krm.2013.6.205

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On the Stokes approximation equations for two-dimensional compressible flows

Qing Yi^1,

1.
College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063

Received: December 31, 2011

Revised: August 31, 2012

Published: February 2013

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Abstract

We deal with the unique global strong solution or classical solution to the Cauchy problem of the 2D Stokes approximation equations for the compressible flows with the density being some positive constant on the far field for arbitrarily large initial data, which may contain vacuum states. First, we prove that the density is bounded from above independently of time. Secondly, we show that if the initial density contains vacuum at least at one point, then the global strong (or classical) solution must blow up as time goes to infinity.

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Mathematics Subject Classification: Primary: 35Q30, 35Q20; Secondary: 76N10.

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