No local double exponential gradient growth in hyperbolic flow for the 2d Euler equation

Hoang, Vu; Radosz, Maria

doi:10.1090/tran/6900

No local double exponential gradient growth in hyperbolic flow for the 2d Euler equation
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by Vu Hoang and Maria Radosz PDF

Trans. Amer. Math. Soc. 369 (2017), 7169-7211 Request permission

Abstract:

We consider smooth, double-odd solutions of the two-dimensional Euler equation in $[-1, 1)^2$ with periodic boundary conditions. This situation is a possible candidate to exhibit strong gradient growth near the origin. We analyze the flow in a small box around the origin in a strongly hyperbolic regime and prove that the compression of the fluid induced by the hyperbolic flow alone is not sufficient to create double-exponential growth of the gradient.

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