Article
On a singular incompressible porous media equation
Author/s | Friedlander, Susan
Gancedo García, Francisco Sun, Weiran Vicol, Vlad |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2012-11 |
Deposit Date | 2016-09-21 |
Published in |
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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 ... 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. |
Project ID. | DMS-0803268
MTM2008-03754 info:eu-repo/grantAgreement/EC/FP7/203138 DMS-0901810 |
Citation | 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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