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

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

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 regim...

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Veröffentlicht in:Transactions of the American Mathematical Society 2017-10, Vol.369 (10), p.7169-7211
Hauptverfasser: HOANG, VU, RADOSZ, MARIA
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description 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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title No local double exponential gradient growth in hyperbolic flow for the 2d Euler equation
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