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Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain

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Li, Y. Charles

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Abstract

We consider the incompressible 2D Euler equations on bounded spatial domain S, and study the solution map on the Sobolev spaces H-k(S) (k > 2). Through an elaborate geometric construction, we show that for any T > 0, the time T solution map u(0) bar right arrow u(T) is nowhere locally uniformly continuous and nowhere Frechet differentiable.

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International Press of Boston

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Mathematics

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Dynamics of Partial Differential Equations

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10.4310/DPDE.2019.v16.n4.a4

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