Continuity of the data-to-solution map for the FORQ equation in Besov Spaces

John Holmes; Feride Tiglay; Ryan Thompson

Continuity of the data-to-solution map for the FORQ equation in Besov Spaces

Analysis of PDEs 2020-10-12 v1

Authors: John Holmes , Feride Tiglay , Ryan Thompson

Abstract

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.

Keywords

FORQ equation data-to-solution map Besov spaces uniform continuity Littlewood-Paley decomposition approximate solutions

Cite

@article{arxiv.2010.04612,
  title  = {Continuity of the data-to-solution map for the FORQ equation in Besov Spaces},
  author = {John Holmes and Feride Tiglay and Ryan Thompson},
  journal= {arXiv preprint arXiv:2010.04612},
  year   = {2020}
}

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