## Exponential growth of the vorticity gradient for the Euler equation on the torus.(English)Zbl 1308.35194

Summary: We prove that there are solutions to the Euler equation on the torus with $$C^{1, \alpha}$$ vorticity and smooth except at one point such that the vorticity gradient grows in $$L^\infty$$ at least exponentially as $$t \to \infty$$. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by A. Kiselev and V. Šverák [Ann. Math. (2) 180, No. 3, 1205–1220 (2014; Zbl 1304.35521)].

### MSC:

 35Q31 Euler equations

Zbl 1304.35521
Full Text:

### References:

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