Singular and regular solutions of a nonlinear parabolic system

Petr Plecháč, Vladimír Šverák

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

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 n ≤ 4. For dimensions n > 4, we present strong numerical evidence supporting the existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding the existence of self-similar singular solutions to a semi-linear heat equation.

Original languageEnglish (US)
Pages (from-to)2083-2097
Number of pages15
JournalNonlinearity
Volume16
Issue number6
DOIs
StatePublished - Nov 2003

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