Clop, AlbertSengupta, Banhirup2025-06-102025-06-102023-05-162737-0690https://hdl.handle.net/2445/221443We 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 quasiconformalmappings13 p.application/pdfengcc-by-nc (c) Finnish Mathematical Society, 2023http://creativecommons.org/licenses/by-nc/4.0/Teoria del transportAplicacions quasiconformesEquacions en derivades parcialsProblemes de valor inicialTransport theoryQuasiconformal mappingsPartial differential equationsInitial value problemsinfo:eu-repo/semantics/article7587162025-06-10info:eu-repo/semantics/openAccess