The regularity of the boundary of vortex patches for some monlinear transport equations

Juan Carlos Cantero; Joan Mateu; Joan Orobitg; Joan Verdera

doi:10.2140/apde.2023.16.1621

The regularity of the boundary of vortex patches for some monlinear transport equations

Juan Carlos Cantero, Joan Mateu, Joan Orobitg, Joan Verdera

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

3 Citas (Scopus)

Resumen

We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in Rⁿ. with velocity field given by convolution of the density with an odd kernel, homogeneous of degree −(n−1) and of class C²(Rⁿ \{0},Rⁿ). This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in R³ and the Cauchy transport equation in the plane are examples.

Idioma original	Inglés
Páginas (desde-hasta)	1621-1650
Número de páginas	30
Publicación	Analysis and PDE
Volumen	16
N.º	7
DOI	https://doi.org/10.2140/apde.2023.16.1621
Estado	Publicada - 2023

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title = "The regularity of the boundary of vortex patches for some monlinear transport equations",

abstract = "We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in Rn. with velocity field given by convolution of the density with an odd kernel, homogeneous of degree −(n−1) and of class C2(Rn \textbackslash{}\{0\},Rn). This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in R3 and the Cauchy transport equation in the plane are examples.",

keywords = "potential theory, transport equation, vortex patch",

author = "Cantero, \{Juan Carlos\} and Joan Mateu and Joan Orobitg and Joan Verdera",

note = "Publisher Copyright: {\textcopyright} 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.",

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AU - Cantero, Juan Carlos

AU - Mateu, Joan

AU - Orobitg, Joan

AU - Verdera, Joan

N1 - Publisher Copyright: © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.

PY - 2023

Y1 - 2023

N2 - We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in Rn. with velocity field given by convolution of the density with an odd kernel, homogeneous of degree −(n−1) and of class C2(Rn \{0},Rn). This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in R3 and the Cauchy transport equation in the plane are examples.

AB - We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in Rn. with velocity field given by convolution of the density with an odd kernel, homogeneous of degree −(n−1) and of class C2(Rn \{0},Rn). This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in R3 and the Cauchy transport equation in the plane are examples.

KW - potential theory

KW - transport equation

KW - vortex patch

UR - https://www.scopus.com/pages/publications/85135090270

U2 - 10.2140/apde.2023.16.1621

DO - 10.2140/apde.2023.16.1621

M3 - Article

AN - SCOPUS:85135090270

SN - 2157-5045

VL - 16

SP - 1621

EP - 1650

JO - Analysis and PDE

JF - Analysis and PDE

IS - 7

ER -

The regularity of the boundary of vortex patches for some monlinear transport equations

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