TY - JOUR
T1 - Vanishing Viscosity Limit to Planar Rarefaction Wave with Vacuum for 3D Compressible Navier-Stokes Equations
AU - Bian , Xin-Xiang
AU - Wang , Yi
AU - Xie , Ling-Ling
JO - Communications in Mathematical Analysis and Applications
VL - 1
SP - 21
EP - 69
PY - 2023
DA - 2023/03
SN - 2
DO - http://doi.org/ 10.4208/cmaa.2022-0020
UR - https://global-sci.org/intro/article_detail/cmaa/21453.html
KW - Compressible Navier-Stokes equations, vanishing viscosity limit, rarefaction wave, vacuum.
AB - <p style="text-align: justify;">The vanishing viscosity limit of the three-dimensional (3D) compressible and isentropic Navier-Stokes equations is proved in the case that the
corresponding 3D inviscid Euler equations admit a planar rarefaction wave solution connected with vacuum states. Moreover, a uniform convergence rate
with respect to the viscosity coefficients is obtained. Compared with previous results on the zero dissipation limit to planar rarefaction wave away from
vacuum states [27, 28], the new ingredients and main difficulties come from
the degeneracy of vacuum states in the planar rarefaction wave in the multi-dimensional setting. Suitable cut-off techniques and some delicate estimates
are needed near the vacuum states. The inviscid decay rate around the planar
rarefaction wave with vacuum is determined by the cut-off parameter and the
nonlinear advection flux terms of 3D compressible Navier-Stokes equations.</p>