Dispersive effects of weakly compressible and fast rotating inviscid fluids

2016/11/18 by Van-Sang Ngo, Ngo, Van-Sang, Stefano Scrobogna +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.1611.06112

openalex publication_date 2016/11/18 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We consider a system describing the motion of an isentropic, inviscid, weakly com-pressible, fast rotating fluid in the whole space R³ , with initial data belonging to H^s(R³) , s \textgreater 5/2. We prove that the system admits a unique local strong solution in L^∞([0, T ]; H^s(R³)) , 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 ε^(--α) , α \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.

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