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2023-05-16

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cc-by-nc (c) Finnish Mathematical Society, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/221443

Nonlinear transport equations and quasiconformal maps

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

Abstract

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

Subject

Teoria del transport, Aplicacions quasiconformes, Equacions en derivades parcials, Problemes de valor inicial

Subject (English)

Transport theory, Quasiconformal mappings, Partial differential equations, Initial value problems

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Articles publicats en revistes (Matemàtiques i Informàtica)

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CLOP, Albert and SENGUPTA, Banhirup. Nonlinear transport equations and quasiconformal maps. Annales Fennici Mathematici. 2023. Vol. 48, num. 1, pags. 375-387. ISSN 2737-0690. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/221443

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