On the blow-up of solutions of the 3-D Euler equations in a bounded domain
On the blow-up of solutions of the 3-D Euler equations in a bounded domain
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DOI：
10.1007/bf02097394
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发表时间：
1993-07
影响因子：
2.4
通讯作者：
A. B. Ferrari
中科院分区：
文献类型：
--
作者：
A. B. Ferrari
证明了：若[0，]是有界单连通区域Ω R ~ 3中不可压Euler方程光滑解u存在的最大区间，则其中ω= ω × u是涡量.这个结果的关键是一个特殊的估计证明在Ω的最大速度梯度的最大涡量和对数项涉及更高的涡量范数。
It is shown that if [0,) is the maximal interval of existence of a smooth solutionuof the incompressible Euler equations in a bounded, simply connected domain ΩR3, then, where ω=∇×uis the vorticity. Crucial to this result is a special estimate proven in Ω of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity.