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Singular and regular solutions of a non-linear parabolic system

Petr Plechac·Vladimir Sverak
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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 $n\leq 4$. For dimensions $n>4$ 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.

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Petr Plechac, Vladimir Sverak. 2003-02-11. Singular and regular solutions of a non-linear parabolic system. https://doi.org/10.1088/0951-7715%2F16%2F6%2F313

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