A Strong Solution of Navier-Stokes Equations with a Rotation Effect for Isentropic Compressible Fluids

We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle, with initial density having a compact support. By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions, we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain. We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains, and derive some uniform bounds of higher order norms, which are independent of the size of the bounded domains. Then we prove the local existence of unique strong solution of the problem in the exterior domain, provided that the initial data satisfy a natural compatibility condition.