Global Existence for an Isotropic Landau Model

Following the recent ideas of Guillen and Silvestre in $[9]$, we prove that the Fisher information is non-increasing along the flow of the isotropic Landau equation. We then use this fact to deduce global existence for the equation ${\mathrm{\partial }}_{t}f=(-\mathrm{\Delta }{)}^{-1}f\cdot \mathrm{\Delta }f+f^2$ under a relatively lax set of conditions on the initial data. In particular, we remove the restrictive radially decreasing assumption of previous works.