Tohoku Mathematical Journal
2020
June
SECOND SERIES VOL. 72, NO. 2

Tohoku Math. J.
72 (2020), 283-297

Title UNIQUENESS THEOREMS FOR THE BOUSSINESQ SYSTEM

Author Lorenzo Brandolese and Jiao He

(Received October 31, 2018)
Abstract. 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.

Mathematics Subject Classification. Primary 76N10, Secondary 35K55, 76D05.
Key words and phrases. Boussinesq approximation, bilinear estimates, Lorentz spaces, Navier--Stokes equations, Besov spaces.

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