UNSPECIFIED (2003) Singular and regular solutions of a nonlinear parabolic system. NONLINEARITY, 16 (6). pp. 2083-2097. ISSN 0951-7715

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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 less than or equal to 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Date:	November 2003
Volume:	16
Number:	6
Number of Pages:	15
Page Range:	pp. 2083-2097
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/8934

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