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

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April 2010, 26(2): 609-623. doi: 10.3934/dcds.2010.26.609

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

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

Received September 2008 Revised August 2009 Published October 2009

Abstract
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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))$.$

Keywords: ill-posed porblems., compressible flows, the Navier-Stokes equations.

Mathematics Subject Classification: Primary: 35Q30, 35M12; Secondary: 76D0.

Citation: Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609

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