John Holmes, Feride Tiglay, Ryan Thompson
Published 2020-10-09Version 1
For Besov spaces $B^s_{p,r}(\rr)$ with $s>\max\{ 2 + \frac1p , \frac52\} $, $p \in (1,\infty]$ and $r \in [1 , \infty)$, it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from $B^s_{p,r}(\rr)$ to $C([0,T]; B^s_{p,r}(\rr))$. The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.
On the continuity of the solution map of the Euler-Poincaré equations in Besov spaces
Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces
Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces
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