Dynamics of Partial Differential Equations

Volume 16 (2019)

Number 4

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

Pages: 383 – 392

DOI: https://dx.doi.org/10.4310/DPDE.2019.v16.n4.a4

Authors

Hasan Inci (Koç Üniversitesi Fen Fakültesi, Rumelifeneri Yolu, Sarıyer, İstanbul, Turkey)

Y. Charles Li (Department of Mathematics, University of Missouri, Columbia, Mo., U.S.A.)

Abstract

We consider the incompressible 2D Euler equations on bounded spatial domain $S$, and study the solution map on the Sobolev spaces $H^k (S)$ $(k \gt 2)$. Through an elaborate geometric construction, we show that for any $T \gt 0$, the time $T$ solution map $u_0 \mapsto u(T)$ is nowhere locally uniformly continuous and nowhere Fréchet differentiable.

Keywords

nowhere-differentiability, nowhere locally uniformly continuous, solution map, Euler equations

2010 Mathematics Subject Classification

35-xx, 76-xx

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Published 30 August 2019