Publication: 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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English
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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.
Source:
Dynamics of Partial Differential Equations
Publisher:
International Press of Boston
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Subject
Mathematics