Illposedness of C2 Vortex Patches
Publication
, Journal Article
Kiselev, A; Luo, X
Published in: Archive for Rational Mechanics and Analysis
June 1, 2023
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.
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Published In
Archive for Rational Mechanics and Analysis
DOI
EISSN
1432-0673
ISSN
0003-9527
Publication Date
June 1, 2023
Volume
247
Issue
3
Related Subject Headings
- General Physics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
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Kiselev, A., & Luo, X. (2023). Illposedness of C2 Vortex Patches. Archive for Rational Mechanics and Analysis, 247(3). https://doi.org/10.1007/s00205-023-01892-7
Kiselev, A., and X. Luo. “Illposedness of C2 Vortex Patches.” Archive for Rational Mechanics and Analysis 247, no. 3 (June 1, 2023). https://doi.org/10.1007/s00205-023-01892-7.
Kiselev A, Luo X. Illposedness of C2 Vortex Patches. Archive for Rational Mechanics and Analysis. 2023 Jun 1;247(3).
Kiselev, A., and X. Luo. “Illposedness of C2 Vortex Patches.” Archive for Rational Mechanics and Analysis, vol. 247, no. 3, June 2023. Scopus, doi:10.1007/s00205-023-01892-7.
Kiselev A, Luo X. Illposedness of C2 Vortex Patches. Archive for Rational Mechanics and Analysis. 2023 Jun 1;247(3).
Published In
Archive for Rational Mechanics and Analysis
DOI
EISSN
1432-0673
ISSN
0003-9527
Publication Date
June 1, 2023
Volume
247
Issue
3
Related Subject Headings
- General Physics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics