A Regularity Criterion of Weak Solutions to the 3D Boussinesq Equations
Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society - Tập 51 - Trang 513-525 - 2019
Tóm tắt
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 $$(u,\theta )$$ becomes regular provided that $$\begin{aligned} (\nabla _{h}{\widetilde{u}},\nabla _{h}\theta )\in L^{1}(0,T;\overset{\cdot }{B }_{\infty ,\infty }^{0}({\mathbb {R}}^{3})) \end{aligned}$$Our results improve and extend the well-known result of Dong and Zhang (Nonlinear Anal 11:2415–2421, 2010) for the Navier–Stokes equations.
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