@article{4b9abfe56ea64e73913fc6d891119f39,
title = "On a singular incompressible porous media equation",
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.",
author = "Susan Friedlander and Francisco Gancedo and Weiran Sun and Vlad Vicol",
note = "Funding Information: S.F. was supported in part by the National Science Foundation (NSF) Grant No. DMS-0803268. F.G. was supported in part by the Grant No. MTM2008-03754 of the Ministerio de Ciencia e Innovation (Spain), the Grant No. StG-203138CDSIF of the European Research Council, and the NSF Grant No. DMS-0901810. V.V. was supported in part by American Mathematical Society (AMS)-Simons travel award.",
year = "2012",
month = nov,
day = "27",
doi = "10.1063/1.4725532",
language = "English (US)",
volume = "53",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "11",
}