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July  2009, 23(3): 755-764. doi: 10.3934/dcds.2009.23.755

Infinite superlinear growth of the gradient for the two-dimensional Euler equation

Sergey A. Denisov 1,

1. 

University of Wisconsin-Madison, Mathematics Department, 480 Lincoln Dr. Madison, WI 53706-1388, United States

Received  February 2008 Revised  July 2008 Published  November 2008

For two-dimensional Euler equation on the torus, we prove that the $L^\infty$ norm of the gradient can grow superlinearly for some infinitely smooth initial data. We also show the exponential growth of the gradient for finite time.
Keywords: growth of the gradient, Two-dimensional Euler equation.
Mathematics Subject Classification: Primary 76B99, secondary 76F99.
Citation: Sergey A. Denisov. Infinite superlinear growth of the gradient for the two-dimensional Euler equation. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 755-764. doi: 10.3934/dcds.2009.23.755
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