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Choi, Kyudong
Fluids Analysis Lab
Research Interests
  • fluid equations, mathematical biology, conservation laws,

Stability of radially symmetric, monotone vorticities of 2D Euler equations

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Title
Stability of radially symmetric, monotone vorticities of 2D Euler equations
Author
Lim, DeokwooChoi, Kyudong
Issue Date
2022-04
Publisher
SPRINGER HEIDELBERG
Citation
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v.61, no.4, pp.120
Abstract
We consider the incompressible Euler equations in R2 when the initial vorticity is bounded, radially symmetric and non-increasing in the radial direction. Such a radial distribution is stationary, and we show that the monotonicity produces stability in some weighted norm related to the angular impulse. For instance, it covers the cases of circular vortex patches and Gaussian distributions. Our stability does not depend on L∞-bound or support size of perturbations. The proof is based on the fact that such a radial monotone distribution minimizes the impulse of functions having the same level set measure.
URI
https://scholarworks.unist.ac.kr/handle/201301/57735
URL
https://link.springer.com/article/10.1007/s00526-022-02231-6
DOI
10.1007/s00526-022-02231-6
ISSN
0944-2669
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