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 Title: L-infinity estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems Authors: Carrillo, J-ASantambrogio, F Item Type: Journal Article Abstract: We prove $L^\infty$ estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial $L^\infty$ norm. This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian solutions without the diffusive term by characteristic methods. Issue Date: 1-Sep-2018 Date of Acceptance: 1-Sep-2017 URI: http://hdl.handle.net/10044/1/60430 DOI: https://dx.doi.org/10.1090/qam/1493 ISSN: 0033-569X Publisher: American Mathematical Society Start Page: 515 End Page: 530 Journal / Book Title: Quarterly of Applied Mathematics Volume: 76 Issue: 3 Copyright Statement: © Copyright 2017 Brown University. First published in Quarterly of Applied Mathematics in 76 (2018), 515-530, published by the American Mathematical Society. Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC) Funder's Grant Number: EP/P031587/1 Keywords: Science & TechnologyPhysical SciencesMathematics, AppliedMathematicsMONGE-AMPERE EQUATIONGRADIENT FLOWTIME AGGREGATIONCRITICAL MASSMODELR-2CHEMOTAXISENERGY0102 Applied MathematicsApplied Mathematics Publication Status: Published Online Publication Date: 2017-11-07 Appears in Collections: MathematicsApplied Mathematics and Mathematical PhysicsFaculty of Natural Sciences