Dispersive effects of weakly compressible and fast rotating inviscid fluids

TL;DR

This paper analyzes the behavior of weakly compressible, fast rotating inviscid fluids, proving local existence and almost global lifespan of solutions independent of initial data size, under rapid rotation conditions.

Contribution

It establishes the existence of unique local solutions and extends their lifespan almost globally using Strichartz estimates, without small initial data assumptions, for weakly compressible, fast rotating fluids.

Findings

Existence of unique local strong solutions in H^s(R^3).

Solutions have almost global lifespan proportional to epsilon^(-alpha).

No smallness condition required on initial data, given sufficient rotation speed.

Abstract

We consider a system describing the motion of an isentropic, inviscid, weakly com-pressible, fast rotating fluid in the whole space R^3 , with initial data belonging to H^s(R^3) , s \textgreater{} 5/2. We prove that the system admits a unique local strong solution in L^$\infty$([0, T ]; H^s(R^3)) , where T is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove that the solution is almost global, i.e. its lifespan is of the order of $\epsilon$^(--$\alpha$) , $\alpha$ \textgreater{} 0, without any smallness assumption on the initial data (the initial data can even go to infinity in some sense), provided that the rotation is fast enough.