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....

ver descrição completa

Detalhes bibliográficos
Autores: Clop, Albert, Sengupta, Banhirup
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/221443
Acesso em linha:https://hdl.handle.net/2445/221443
Access Level:acceso abierto
Palavra-chave:Teoria del transport
Aplicacions quasiconformes
Equacions en derivades parcials
Problemes de valor inicial
Transport theory
Quasiconformal mappings
Partial differential equations
Initial value problems
Descrição
Resumo: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