Global well-posedness and asymptotic behavior for Navier-Stokes-Coriolis equations in homogeneous Besov spaces

TL;DR

This paper proves the global existence, uniqueness, and asymptotic behavior of solutions to the 3D Navier-Stokes equations with Coriolis force in homogeneous Besov spaces, especially for large rotation speeds.

Contribution

It establishes well-posedness results in homogeneous Besov spaces for the Navier-Stokes-Coriolis equations and analyzes their asymptotic behavior as rotation speed increases.

Findings

Global solutions exist and are unique for large rotation speeds.

Solutions exhibit specific asymptotic behavior as rotation speed tends to infinity.

The initial data class is characterized using the Stokes-Coriolis semigroup and Besov spaces.

Abstract

We are concerned with the $3$D-Navier-Stokes equations with Coriolis force. Existence and uniqueness of global solutions in homogeneous Besov spaces are obtained for large speed of rotation. In the critical case of the regularity, we consider a suitable initial data class whose definition is based on the Stokes-Coriolis semigroup and Besov spaces. Moreover, we analyze the asymptotic behavior of solutions in that setting as the speed of rotation goes to infinity.