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On a singular incompressible porous media equation

 

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Author: Friedlander, Susan
Gancedo García, Francisco
Sun, Weiran
Vicol, Vlad
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2012-11
Published in: Journal of Mathematical Physics, 53 (115602)
Document type: Article
Abstract: This paper considers a family of active scalar equations with transport velocities which are more singular by a derivative of order β than the active scalar. We prove that the equations with 0 < β ≤ 2 are Lipschitz ill-posed for regular initial data. On the contrary, when 0 < β < 1 we show local well-posedness for patch-type weak solutions.
Cite: Friedlander, S., Gancedo García, F., Sun, W. y Vicol, V. (2012). On a singular incompressible porous media equation. Journal of Mathematical Physics, 53 (115602)
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URI: http://hdl.handle.net/11441/45196

DOI: 10.1063/1.4725532

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