Nonlinear transport equations and quasiconformal maps

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....

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Detalles Bibliográficos
Autores: Clop, Albert, Sengupta, Banhirup
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/221443
Acceso en línea:https://hdl.handle.net/2445/221443
Access Level:acceso abierto
Palabra clave:Teoria del transport
Aplicacions quasiconformes
Equacions en derivades parcials
Problemes de valor inicial
Transport theory
Quasiconformal mappings
Partial differential equations
Initial value problems
Descripción
Sumario: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