Illposedness of C<sup>2</sup> Vortex Patches

Loading...
Thumbnail Image

Date

2023-06-01

Journal Title

Journal ISSN

Volume Title

Repository Usage Stats

2
views
24
downloads

Citation Stats

Abstract

It is well known that vortex patches are wellposed in C1,α if 0 < α< 1 . In this paper, we prove the illposedness of C2 vortex patches. The setup is to consider the vortex patches in Sobolev spaces W2,p where the curvature of the boundary is Lp integrable. In this setting, we show the persistence of W2,p regularity when 1 < p< ∞ and construct C2 initial patch data for which the curvature of the patch boundary becomes unbounded immediately for t> 0 , though it regains C2 regularity precisely at all integer times without being time periodic. The key ingredient is the evolution equation for the curvature, the dominant term in which turns out to be linear and dispersive.

Department

Description

Provenance

Subjects

Citation

Published Version (Please cite this version)

10.1007/s00205-023-01892-7

Publication Info

Kiselev, A, and X Luo (2023). Illposedness of C2 Vortex Patches. Archive for Rational Mechanics and Analysis, 247(3). 10.1007/s00205-023-01892-7 Retrieved from https://hdl.handle.net/10161/29538.

This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.

Scholars@Duke

Kiselev

Alexander A. Kiselev

William T. Laprade Distinguished Professor of Mathematics

My current research interests focus on mathematical fluid mechanics and mathematical biology.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators. 


Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.