Well-posedness for the Boussinesq system in critical spaces via maximal regularity

Brandolese, Lorenzo; Monniaux, Sylvie

doi:10.5802/aif.3523

Well-posedness for the Boussinesq system in critical spaces via maximal regularity
[Caractère bien posé du système de Boussinesq dans les espaces critiques via la régularité maximale]

Brandolese, Lorenzo ¹ ; Monniaux, Sylvie ²

¹ Institut Camille Jordan Université de Lyon, Université Lyon 1 43 bd. du 11 Novembre 69622 Villeurbanne Cedex (France)
² Aix Marseille Univ, CNRS, I2M Marseille (France)

Annales de l'Institut Fourier, Tome 73 (2023) no. 1, pp. 1-20.

Résumé
Abstract

Nous prouvons des résultats d’existence et unicité pour le système de Boussinesq dans $ℝ^{3}$ dans $𝒞 ([0, T], L^{3} {(ℝ^{3})}^{3}) \times L^{2} (0, T; L^{3 / 2} (ℝ^{3}))$ , espace critique pour ce système.

We establish the existence and the uniqueness for the Boussinesq system in $ℝ^{3}$ in the critical space $𝒞 ([0, T], L^{3} {(ℝ^{3})}^{3}) \times L^{2} (0, T; L^{3 / 2} (ℝ^{3}))$ .

Reçu le : 2020-12-03
Révisé le : 2021-05-07
Accepté le : 2021-06-23
Publié le : 2023-05-12

DOI : 10.5802/aif.3523

Classification : 35A02, 76D03, 35Q35
Keywords: Maximal regularity, Boussinesq system, critical space, uniqueness, existence
Mot clés : Régularité maximale, système de Boussinesq, espaces critiques, unicité, existence

Affiliations des auteurs :

Brandolese, Lorenzo ¹ ; Monniaux, Sylvie ²

¹ Institut Camille Jordan Université de Lyon, Université Lyon 1 43 bd. du 11 Novembre 69622 Villeurbanne Cedex (France)
² Aix Marseille Univ, CNRS, I2M Marseille (France)

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Well-posedness for the {Boussinesq} system in critical spaces via maximal regularity},
     journal = {Annales de l'Institut Fourier},
     pages = {1--20},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Brandolese, Lorenzo; Monniaux, Sylvie. Well-posedness for the Boussinesq system in critical spaces via maximal regularity. Annales de l'Institut Fourier, Tome 73 (2023) no. 1, pp. 1-20. doi : 10.5802/aif.3523. https://aif.centre-mersenne.org/articles/10.5802/aif.3523/

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