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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
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