Nonlinear transport equations and quasiconformal maps

Authors

  • Albert Clop Universitat de Barcelona, Department of Mathematics and Computer Science
  • Banhirup Sengupta Universitat Autònoma de Barcelona, Departament de Matemàtiques

DOI:

https://doi.org/10.54330/afm.130026

Keywords:

Quasiconformal map, transport equation, active scalar

Abstract

We prove existence of solutions to a nonlinear transport equation in the plane, for which the velocity field is obtained as the convolution of the classical Cauchy kernel with the unknown. Even though the initial datum is bounded and compactly supported, the velocity field may have unbounded divergence. The proof is based on the compactness property of quasiconformal mappings.

 

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Published

2023-05-16

Issue

Vol. 48 No. 1 (2023)

Section

Articles

License

Copyright (c) 2023 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Clop, A., & Sengupta, B. (2023). Nonlinear transport equations and quasiconformal maps. Annales Fennici Mathematici, 48(1), 375-387. https://doi.org/10.54330/afm.130026