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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2402.11967 |
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| _version_ | 1866909293244055552 |
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| author | Charve, Frédéric |
| author_facet | Charve, Frédéric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data Charve, Frédéric Analysis of PDEs 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. |
| title | New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.11967 |