Local existence and blow-up criterion for the Boussinesq equations

Local existence and blow-up criterion for the Boussinesq equations
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DOI：
10.1017/s0308210500026810
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发表时间：
1997
期刊：
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
影响因子：
--
通讯作者：
D. Chae;Hee-Seok Nam
D. Chae;Hee-Seok Nam
中科院分区：
其他
文献类型：
--
作者：
D. Chae;Hee-Seok Nam

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本文证明了Boussinesq方程光滑解的局部存在唯一性。我们还得到了这些光滑解的爆破准则。这表明被动标量梯度的最大范数控制了Boussinesq方程光滑解的崩溃。作为该准则的一个应用，我们在零外力的情形下证明了整体光滑解的存在性。
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.