Singular and regular solutions of a non-linear parabolic system
Analysis of PDEs
2009-11-10 v1
Abstract
We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions . For dimensions we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.
Cite
@article{arxiv.math/0302129,
title = {Singular and regular solutions of a non-linear parabolic system},
author = {Petr Plechac and Vladimir Sverak},
journal= {arXiv preprint arXiv:math/0302129},
year = {2009}
}
Comments
16 pages