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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2083-2097 |
| Number of pages | 15 |
| Journal | Nonlinearity |
| Volume | 16 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 2003 |