Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow

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• 作者：Xiaoqian Xu ^{xxu@math.wisc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：2D Euler equation ; Hyperbolic flow ; Green function
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：439
• 期：2
• 页码：594-607
• 全文大小：364 K

文摘

We construct initial data for the two-dimensional Euler equation in a bounded smooth symmetric domain such that the gradient of vorticity in L^∞$L^{\infty }$ grows as a double exponential in time, for all time. Our construction is based on the recent result by Kiselev and Šverák [9].