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arXiv · 1602.08259

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

Stefano Scrobogna
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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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Stefano Scrobogna. 2016-02-26. Derivation of limit equation for a perturbed 3D periodic Boussinesq system. https://arxiv.org/abs/1602.08259

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