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Zbl 1171.35342
Fan, Jishan; Zhou, Yong
A note on regularity criterion for the 3D Boussinesq system with partial viscosity.
(English)
[J] Appl. Math. Lett. 22, No. 5, 802-805 (2009). ISSN 0893-9659

Summary: We prove a regularity criterion for $\omega := \text{curl }u\in L^1(0,T;\dot B^0_{\infty,\infty})$ for the 3D Boussinesq system with partial viscosity. Here $u$ is the velocity, $\omega$ is the vorticity and $\dot B^0_{\infty,\infty}$ denotes the homogeneous Besov space.
MSC 2000:
*35B65 Smoothness of solutions of PDE
35Q35 Other equations arising in fluid mechanics

Keywords: Besov spaces; partial viscosity

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