@Article{CMAA-2-21,
author = {Bian , Xin-XiangWang , Yi and Xie , Ling-Ling},
title = {Vanishing Viscosity Limit to Planar Rarefaction Wave with Vacuum for 3D Compressible Navier-Stokes Equations},
journal = {Communications in Mathematical Analysis and Applications},
year = {2023},
volume = {2},
number = {1},
pages = {21--69},
abstract = {<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>},
issn = {2790-1939},
doi = {https://doi.org/ 10.4208/cmaa.2022-0020},
url = {http://global-sci.org/intro/article_detail/cmaa/21453.html}
}