Petr Plechác and Vladimír Sverák 2003 Nonlinearity 16 2083 doi:10.1088/0951-7715/16/6/313
Petr Plechác1 and Vladimír Sverák2
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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.
02.30.Jr Partial differential equations
47.10.ad Navier-Stokes equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
34B16 Singular nonlinear boundary value problems
Issue 6 (November 2003)
Received 12 February 2003, in final form 1 July 2003
Published 5 September 2003
Petr Plechác and Vladimír Sverák 2003 Nonlinearity 16 2083
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