New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data

Abstract

In our previous work dedicated to the strongly stratified Boussinesq system, we obtained for the first time a limit system (when the froude number ε goes to zero) that depends on the thermal diffusivity ν ′ (other works obtained a limit system only depending on the visosity ν). To reach those richer asymptotics we had to consider an unusual initial data which is the sum of a function depending on the full space variable and a function only depending on the vertical coordinate, and we studied the convergence of the weak Leray-type solutions. In the present article we extend these results to the strong Fujita-Kato-type solutions. We obtain far better convergence rates (in ε) for ill-prepared initial data with very large oscillating part of size some negative power of the small parameter ε. The main difficulties come from the anisotropy induced by the presence of x3-depending functions.
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Dates and versions

hal-04459374 , version 1 (15-02-2024)

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Frédéric Charve. New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data. 2024. ⟨hal-04459374⟩
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