Local well-posedness of isentropic compressible Navier–Stokes equations with vacuum
Huajun Gong, Jinkai Li, Xiangao Liu, Xiaotao Zhang
Abstract
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 date 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 literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.
Topics & Concepts
Isentropic processCompressibilityInitial value problemMathematicsMathematical analysisNon-dimensionalization and scaling of the Navier–Stokes equationsCauchy problemNavier–Stokes equationsPhysicsMechanicsNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential Equations