An ill-posed problem for the Navier-Stokes equations for compressible flows
An ill-posed problem for the Navier-Stokes equations for compressible flows
We consider the Navier-Stokes equations for the motion of a compressible, viscous, isentropicfluid 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))$.$