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2003 Nonlinearity 16 2083-2097 doi: 10.1088/0951-7715/16/6/313
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Recommended by E S Titi
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.
Mathematics Subject Classification: 35K55, 35B05, 76A02
Print publication: Issue 6 (November 2003) |
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