The paper deals with the regularity criteria for the weak solutions to the 3D Boussinesq equations in terms of the partial derivatives in Besov spaces. It is proved that the weak solution ((u, heta )) becomes regular provided that $$egin{aligned} ( abla _{h}{widetilde{u}}, abla _{h} heta )in L^{1}(0,T;overset{cdot }{B }_{infty ,infty }^{0}({mathbb {R}}^{3})) end{aligned}$$
A Regularity Criterion of Weak Solutions to the 3D Boussinesq Equations
Ragusa, Maria Alessandra
2020-01-01
Abstract
The paper deals with the regularity criteria for the weak solutions to the 3D Boussinesq equations in terms of the partial derivatives in Besov spaces. It is proved that the weak solution ((u, heta )) becomes regular provided that $$egin{aligned} ( abla _{h}{widetilde{u}}, abla _{h} heta )in L^{1}(0,T;overset{cdot }{B }_{infty ,infty }^{0}({mathbb {R}}^{3})) end{aligned}$$File in questo prodotto:
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