The Method of a-Contraction with Shifts Used for Long-Time Behavior Toward Viscous Shock
摘要
We revisit the method of a-contraction with shifts used for long-time behavior of barotropic Navier-Stokes flows perturbed from a Riemann shock. For the usage of the method of a-contraction with shifts, we do not employ the effective velocity h variable even for higher order estimates. This approach would be important when handling the barotropic Navier-Stokes system with other effects, for example, such as capillary effect and boundary effect.