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Local existence and blow-up criterion for the Boussinesq equations
- Issue Date
- May-1997
- Publisher
- ROYAL SOC EDINBURGH
- Citation
- PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v.127, no.5, pp 935 - 946
- Pages
- 12
- Journal Title
- PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
- Volume
- 127
- Number
- 5
- Start Page
- 935
- End Page
- 946
- ISSN
- 0308-2105
1473-7124
- Abstract
- 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.
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