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

Lorenzo Brandolese (1, 2) , Sylvie Monniaux (3)

1 ICJ - Institut Camille Jordan
2 EDPA - Équations aux dérivées partielles, analyse
3 I2M - Institut de Mathématiques de Marseille

We establish the existence and the uniqueness for the Boussinesq system in the whole 3D space in the critical space of continuous in time with values in the power 3 integrable in space functions for the velocity and square integrable in time with values in the power 3/2 integrable in space.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Lorenzo Brandolese, Sylvie Monniaux. Well-posedness for the Boussinesq system in critical spaces via maximal regularity. Annales de l'Institut Fourier, 2023, 73 (1), pp.1-20. ⟨10.5802/aif.3523⟩. ⟨hal-03038112v2⟩