2024/05/20 by Liao, Xian, Zodji, Sagbo Marcel · 2 citations
#35A01 #35A02 #35Q30 #35R35 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2405.11900
We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as blocks, for less regular initial data where the vacuum is permitted, the global-in-time well-posedness follows from the energy estimates and the propagated striated regularity of the density function, if the bulk viscosity coefficient is large enough in the two dimensional case. The global-in-time well-posedness holds also true in the three dimensional case, provided with large bulk viscosity coefficient together with small initial energy. This solves the density-patch problem in the exterior domain for the compressible model with W2,p-Interfaces. Finally, the singular incompressible limit toward the inhomogenous incompressible model when the bulk viscosity coefficient tends to infinity is obtained.