Gong, Huajun; Li, Jinkai; Liu, Xian-Gao; Zhang, Xiaotao Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. (English) Zbl 1467.35242 Commun. Math. Sci. 18, No. 7, 1891-1909 (2020). Summary: In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial data being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many works concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum. Cited in 11 Documents MSC: 35Q30 Navier-Stokes equations 35D35 Strong solutions to PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:isentropic Navier-Stokes equations; local well-posedness; vacuum; without compatibility condition PDFBibTeX XMLCite \textit{H. Gong} et al., Commun. Math. Sci. 18, No. 7, 1891--1909 (2020; Zbl 1467.35242) Full Text: DOI arXiv