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arXiv · 2403.10810

Global Existence for an Isotropic Landau Model

David Bowman·Sehyun Ji
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Abstract

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 $\partial_t f = (-\Delta)^{-1}f \cdot \Delta f + f^2$ under a relatively lax set of conditions on the initial data. In particular, we remove the restrictive radially decreasing assumption of previous works.

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David Bowman, Sehyun Ji. 2024-03-16. Global Existence for an Isotropic Landau Model. https://arxiv.org/abs/2403.10810

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