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The regularity of the
boundary of vortex patches for some nonlinear transport
equations
Juan Carlos Cantero, Joan Mateu, Joan Orobitg and Joan Verdera |
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Vol. 16 (2023), No. 7, 1621–1650
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Abstract |
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We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in with velocity field given by convolution of the density with an odd kernel, homogeneous of degree and of class . This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in and the Cauchy transport equation in the plane are examples. |
Keywords
transport equation, vortex patch, potential theory
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Mathematical Subject Classification
Primary: 35Q31, 35Q35, 35Q49, 35K59, 35L60
Secondary: 42B20
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Milestones
Received: 10 March 2021
Revised: 27 November 2021
Accepted: 28 February 2022
Published: 21 September 2023
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Authors |
| Juan Carlos Cantero | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona Barcelona Catalonia |
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| Joan Mateu | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona and Centre de Recerca Matemàtica Barcelona Catalonia |
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| Joan Orobitg | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona and Centre de Recerca Matemàtica Barcelona Catalonia |
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| Joan Verdera | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona and Centre de Recerca Matemàtica Barcelona Catalonia |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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