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Local existence and blow-up criterion for the Boussinesq equations

Published online by Cambridge University Press:  14 November 2011

Dongho Chae  and
Hee-Seok Nam
Dongho Chae
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea e-mail: [email protected]
Hee-Seok Nam
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea
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Synopsis

In this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions in the case of zero external force.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 935 - 946
Copyright
Copyright © Royal Society of Edinburgh 1997

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