Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
The regularity of the boundary of vortex patches for some nonlinear transport equations

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

Vol. 16 (2023), No. 7, 1621–1650
Abstract

We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in n with velocity field given by convolution of the density with an odd kernel, homogeneous of degree  (n 1) and of class C2(n {0}, n). This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in 3 and the Cauchy transport equation in the plane are examples.

Keywords
transport equation, vortex patch, potential theory
Mathematical Subject Classification
Primary: 35Q31, 35Q35, 35Q49, 35K59, 35L60
Secondary: 42B20
Milestones
Received: 10 March 2021
Revised: 27 November 2021
Accepted: 28 February 2022
Published: 21 September 2023
Authors
Juan Carlos Cantero
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Barcelona
Catalonia
Joan Mateu
Departament de Matemàtiques
Universitat Autònoma de Barcelona and Centre de Recerca Matemàtica
Barcelona
Catalonia
Joan Orobitg
Departament de Matemàtiques
Universitat Autònoma de Barcelona and Centre de Recerca Matemàtica
Barcelona
Catalonia
Joan Verdera
Departament de Matemàtiques
Universitat Autònoma de Barcelona and Centre de Recerca Matemàtica
Barcelona
Catalonia

Open Access made possible by participating institutions via Subscribe to Open.