Exponential growth of the vorticity gradient for the Euler equation on the torus

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We prove that there are solutions to the Euler equation on the torus with C¹,α vorticity and smooth except at one point such that the vorticity gradient grows in L∞ at least exponentially as t→∞. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Sverak.