Abstract
We consider smooth, double-odd solutions of the two-dimensional Euler equation in [ − 1 , 1 ) 2 [-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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