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....
| Autores: | , |
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| 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 |
| 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 |
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