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Singular and regular solutions of a nonlinear parabolic system
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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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | November 2003 | ||||
Dates: |
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Volume: | 16 | ||||
Number: | 6 | ||||
Number of Pages: | 15 | ||||
Page Range: | pp. 2083-2097 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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