Nonlinear transport equations and quasiconformal maps
Avainsanat:
Quasiconformal map, transport equation, active scalarAbstrakti
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.
Viittaaminen
Clop, A., & Sengupta, B. (2023). Nonlinear transport equations and quasiconformal maps. Annales Fennici Mathematici, 48(1), 375–387. https://doi.org/10.54330/afm.130026
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