Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain
| Autor: | Inci, Hasan, Li, Y. Charles |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $u_0 \mapsto u(T)$ is nowhere locally uniformly continuous and nowhere Fr\'echet differentiable. Comment: 14 pages |
| Databáze: | arXiv |
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