Well-Posedness of the Generalized Proudman-Johnson Equation Without Viscosity
Well-Posedness of the Generalized Proudman-Johnson Equation Without Viscosity
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DOI：
10.1007/s00021-007-0247-9
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发表时间：
2009-03-01
影响因子：
1.3
通讯作者：
Okamoto, Hisashi
中科院分区：
文献类型：
--
作者：
Okamoto, Hisashi
本文考虑了由朱京辉和作者从Navier-Stokes方程出发导出的广义Proudman-Johnson方程，在忽略粘性和施加周期性边界条件的情况下。该方程具有两个非线性项：对流项和拉伸项。我们证明，如果拉伸项在下面指定的意义下是弱的，则解在时间上全局存在。当拉伸项较强时，我们还讨论了爆破解。
The generalized Proudman-Johnson equation, which was derived from the Navier-Stokes equations by Jinghui Zhu and the author, are considered in the case where the viscosity is neglected and the periodic boundary condition is imposed. The equation possesses two nonlinear terms: the convection and stretching terms. We prove that the solution exists globally in time if the stretching term is weak in the sense to be specified below. We also discuss on blow-up solutions when the stretching term is strong.