REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS
1999 ◽
Vol 09
(09)
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pp. 1323-1332
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Keyword(s):
Blow Up
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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.