Global existence theorem for the three-dimensional isentropic compressible Navier-Stokes flow in the exterior of a rotating obstacle

TL;DR

This paper proves the global existence and uniqueness of classical solutions for 3D isentropic compressible Navier-Stokes equations around a rotating obstacle with small initial mass, allowing large oscillations in initial data and obstacle rotation.

Contribution

It establishes the first global existence result for this problem with rotating effects and vacuum conditions, accommodating large oscillations in initial data and obstacle angular velocity.

Findings

Global existence and uniqueness of solutions are proven.

Results hold for large oscillations in initial data and obstacle rotation.

The study extends understanding of compressible flows around rotating obstacles.

Abstract

In this paper, we consider the initial-boundary value problem of three-dimensional isentropic compressible Navier-Stokes equations with rotating effect terms in an exterior domain with Navier-slip boundary condition and with far-field vacuum. This problem is related to the motion of the compressible viscous flow past a rotating obstacle. We establish the global existence and uniqueness of classical solutions, provided that the initial mass is small. The initial data and the angular velocity of the obstacle are allowed to have large oscillations.