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

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.