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,∇θ)∈L2(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 θ.

On the Regularity of Weak Solutions of the Boussinesq Equations in Besov Spaces / Barbagallo, A.; Gala, S.; Ragusa, M. A.; Thera, M.. - In: VIETNAM JOURNAL OF MATHEMATICS. - ISSN 2305-221X. - 49:3(2021), pp. 637-649. [10.1007/s10013-020-00420-4]

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

Barbagallo A.;
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,∇θ)∈L2(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 θ.
2021
On the Regularity of Weak Solutions of the Boussinesq Equations in Besov Spaces / Barbagallo, A.; Gala, S.; Ragusa, M. A.; Thera, M.. - In: VIETNAM JOURNAL OF MATHEMATICS. - ISSN 2305-221X. - 49:3(2021), pp. 637-649. [10.1007/s10013-020-00420-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/829339
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