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

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