Global strong solutions to the compressible Navier--Stokes--Coriolis system for large data

TL;DR

This paper proves the existence of unique global strong solutions to the 3D compressible Navier--Stokes--Coriolis system with large data, leveraging dispersive effects from high rotation speeds and low Mach numbers.

Contribution

It overcomes previous difficulties by constructing solutions in critical Besov spaces, accounting for the dispersive effects of the Coriolis force and acoustic waves.

Findings

Global strong solutions exist for large data with high rotation speed and low Mach number.

Solutions are constructed in scaling critical Besov spaces.

Dispersive effects enable handling of low-frequency nonlinear estimates.

Abstract

We consider the compressible Navier--Stokes system with the Coriolis force on the $3$D whole space. In this model, the Coriolis force causes the linearized solution to behave like a $4$th order dissipative semigroup $\{ e^{-t\Delta^2} \}_{t>0}$ with slower time decay rates than the heat kernel, which creates difficulties in nonlinear estimates in the low-frequency part and prevents us from constructing the global strong solutions by following the classical method. On account of this circumstance, the existence of unique global strong solutions has been open even in the classical Matsumura--Nishida framework. In this paper, we overcome the aforementioned difficulties and succeed in constructing a unique global strong solution in the framework of scaling critical Besov spaces. Furthermore, our result also shows that the global solution is constructed for arbitrarily large initial data provided that the speed of the rotation is high and the Mach number is low enough by focusing on the dispersive effect due to the mixture of the Coriolis force and acoustic wave.