The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space Ḃ∞,∞−1(R3), that, if the solution of the Boussinesq equation (1) below (starting with an initial data in H2) is such that (∇u,∇ϵ)ϵL2(0,T;Ḃ∞,∞−1(R3)), then the solution remains smooth forever after T. In this contribution, we prove the same result for weak solutions just by assuming the condition on the velocity u and not on the temperature ϵ.

On the Regularity of Weak Solutions of the Boussinesq Equations in Besov Spaces

Barbagallo A.
;
Thera M.
2021

Abstract

The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space Ḃ∞,∞−1(R3), that, if the solution of the Boussinesq equation (1) below (starting with an initial data in H2) is such that (∇u,∇ϵ)ϵL2(0,T;Ḃ∞,∞−1(R3)), then the solution remains smooth forever after T. In this contribution, we prove the same result for weak solutions just by assuming the condition on the velocity u and not on the temperature ϵ.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/889362
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