an:06370007
Zbl 1308.35194
Zlato??, Andrej
Exponential growth of the vorticity gradient for the Euler equation on the torus
EN
Adv. Math. 268, 396-403 (2015).
00338447
2015
j
35Q31
Euler equations on the torus; vorticity gradient growth
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 \textit{A. Kiselev} and \textit{V. ??ver??k} [Ann. Math. (2) 180, No. 3, 1205--1220 (2014; Zbl 1304.35521)].
Zbl 1304.35521