Dynamics of Partial Differential Equations
Volume 16 (2019)
Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain
Pages: 383 – 392
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.
nowhere-differentiability, nowhere locally uniformly continuous, solution map, Euler equations
2010 Mathematics Subject Classification
Published 30 August 2019