Global solutions for a supercritical drift-diffusion equation

@article{Burczak2016GlobalSF,
title={Global solutions for a supercritical drift-diffusion equation},
author={Jan Burczak and Rafael Granero-Belinch'on},
year={2016},
volume={295},
pages={334-367}
}
• Published 2 July 2015
• Mathematics
23 Citations
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Critical Keller–Segel meets Burgers on S1: large-time smooth solutions
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We show that solutions to the parabolic–elliptic Keller–Segel system on S1 with critical fractional diffusion (−Δ) 12 remain smooth for any initial data and any positive time. This disproves, at

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On a generalized, doubly parabolic Keller-Segel system in one spatial dimension
• Mathematics
• 2014
We study a doubly parabolic Keller-Segel system in one spatial dimension, with diffusions given by fractional laplacians. We obtain several local and global well-posedness results for the subcritical
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In this paper, we study the Cauchy problem for the Keller–Segel system with fractional diffusion generalizing the Keller–Segel model of chemotaxis for the initial data (u0,v0) in critical
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Critical Keller–Segel meets Burgers on S1: large-time smooth solutions
• Mathematics
• 2016
We show that solutions to the parabolic–elliptic Keller–Segel system on S1 with critical fractional diffusion (−Δ) 12 remain smooth for any initial data and any positive time. This disproves, at
Further Properties of a Continuum of Model Equations with Globally Defined Flux
To develop an understanding of singularity formation in vortex sheets, we consider model equations that exhibit shared characteristics with the vortex sheet equation but are slightly easier to