Singular and regular solutions of a nonlinear parabolic system
UNSPECIFIED. (2003) Singular and regular solutions of a nonlinear parabolic system. NONLINEARITY, 16 (6). pp. 2083-2097. ISSN 0951-7715Full text not available from this repository.
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|
|Number of Pages:||15|
|Page Range:||pp. 2083-2097|
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