Well-posedness for the Boussinesq system in critical spaces via maximal regularity
Brandolese, Lorenzo1; Monniaux, Sylvie2
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, Online first, 20 p.

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 )×L 2 (0,T;L 3/2 (ℝ 3 )).

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 )×L 2 (0,T;L 3/2 (ℝ 3 )), espace critique pour ce système.

Received:
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Accepted:
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DOI: 10.5802/aif.3523
Classification: 35A02, 76D03, 35Q35
Keywords: Maximal regularity, Boussinesq system, critical space, uniqueness, existence
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) 
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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, Online first, 20 p.

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