Uniqueness theorems for the Boussinesq system

Lorenzo Brandolese (1, 2) , Jiao He (1, 2)

1 EDPA - Équations aux dérivées partielles, analyse
2 ICJ - Institut Camille Jordan

We address the uniqueness problem for mild solutions of the Boussinesq system in $\mathbb{R}^3$. We provide several uniqueness classes on the velocity and the temperature, generalizing in this way the classical $C([0, T ]; L^3 (\mathbb{R}^3))$-uniqueness result for mild solutions of the Navier-Stokes equations.

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brandolese, Jiao He. Uniqueness theorems for the Boussinesq system. Tohoku mathematical journal, In press, ⟨10.2748/tmj/1593136822⟩. ⟨hal-01908286v2⟩