Derivation of limit equation for a perturbed 3D periodic Boussinesq system

2016/02/26 by Stefano Scrobogna, Scrobogna, Stefano
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1602.08259

openalex publication_date 2016/02/26 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

We consider a system describing the long-time dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well posed with respect to a H^s, s>1/2 Sobolev regularity. Moreover if the Froude number converges to zero we prove that the solutions of the aforementioned system converge (strongly) to a stratified three-dimensional Navier-Stokes system. No smallness assumption is assumed on the initial data.

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