Geodesic
Nonlinear transport equations and quasiconformal maps
Albert Clop1 ; Banhirup Sengupta2
1 Universitat de Barcelona, Department of Mathematics and Computer Science
2 Universitat Autònoma de Barcelona, Departament de Matemàtiques
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 375-387.

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We prove existence of solutions to a nonlinear transport equation in the plane, for which the velocity field is obtained as the convolution of the classical Cauchy kernel with the unknown. Even though the initial datum is bounded and compactly supported, the velocity field may have unbounded divergence. The proof is based on the compactness property of quasiconformal mappings.  
DOI : 10.54330/afm.130026
Keywords: Quasiconformal map, transport equation, active scalar

Albert Clop 1 ; Banhirup Sengupta 2

1 Universitat de Barcelona, Department of Mathematics and Computer Science
2 Universitat Autònoma de Barcelona, Departament de Matemàtiques 
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Albert Clop; Banhirup Sengupta. Nonlinear transport equations and quasiconformal maps. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 375-387. doi : 10.54330/afm.130026. http://geodesic.mathdoc.fr/articles/10.54330/afm.130026/

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