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Infinite superlinear growth of the gradient for the two-dimensional Euler equation. (English) Zbl 1156.76009
Summary: 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.

MSC:
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
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