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Zbl 1034.35113
Ishimura, Naoyuki; Morimoto, Hiroko
Remarks on the blow-up criterion for the 3-D Boussinesq equations. (English)
[J] Math. Models Methods Appl. Sci. 9, No. 9, 1323-1332 (1999). ISSN 0218-2025

Summary: We consider the problem of blow-up of smooth solutions for the 3-D Boussinesq equations. Owing to the viscosity, we prove that the maximum norm of the gradient of vorticity controls the breakdown of the solutions; the scalar temperature function is shown to be irrelevant to the breakdown.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
35B40 Asymptotic behavior of solutions of PDE
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: blow-up of smooth solutions; Boussinesq equations

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