Spatial Asymptotic Profiles of Solutions to the Navier-Stokes System in a Rotating Frame with Fast Decaying Data

Abstract

The nonstationary Navier-Stokes system for a viscous, incompressible fluid influenced by a Coriolis force in the whole space ${\mathbb R}^3$ is considered at large distances. The solvability of the corresponding integral equations of these equations in weighted $L^\infty$-spaces is established. Furthermore, the leading terms of the asymptotic profile of the solution at fixed time $t \gt 0$ for $|x| \gt t$ and far from the axis of rotation are investigated.