For the half-line outflow problem, small perturbations of weak viscous shocks converge to the shock up to a dynamical shift whose speed decays to zero.
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Asymptotic behavior toward viscous shocks for the outflow problem of barotropic Navier-Stokes equations
For the half-line outflow problem, small perturbations of weak viscous shocks converge to the shock up to a dynamical shift whose speed decays to zero.