An ill-posed problem for the Navier-Stokes equations for compressible flows

Misha Perepelitsa

doi:10.3934/dcds.2010.26.609

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2010, Volume 26, Issue 2: 609-623. Doi: 10.3934/dcds.2010.26.609

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An ill-posed problem for the Navier-Stokes equations for compressible flows

Misha Perepelitsa^1,

1.
University of Houston, Department of Mathematics, 651 PGH, Houston, Texas 77204-3008

Received: September 1, 2008

Revised: August 1, 2009

Published online: October 1, 2009

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Abstract

We consider the Navier-Stokes equations for the motion of a compressible, viscous, isentropic fluid in a half-space H². We prove that under the no-slip boundary conditions, the initial-boundary value problem is ill-posed in the space ($\rho$($t,\cdot$)$,\grad_x\u$($t,\cdot$))$\in$($L^\infty_x$(H²)$\times L^\infty_x$(H²))$.$

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Mathematics Subject Classification: Primary: 35Q30, 35M12; Secondary: 76D03.

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