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- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Nature Switzerland AG 2020
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-019-00556-y
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we prove that the 2D viscous shallow water equations are ill-posed in the critical Besov spaces B˙p,12p-1(R2)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\dot{B}^{\frac{2}{p}-1}_{p,1}({\mathbb {R}}^2)$$\end{document} with p>4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$p>4$$\end{document}. Our proof mainly depends on the method introduced by Bourgain and Pavlović (J Funct Anal 255:2233–2247, 2008) and Chen et al. (Rev Mat Iberoam 31:1375–1402, 2015).
Journal
Journal of Evolution Equations – Springer Journals
Published: Jan 8, 2020