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arXiv · 2309.15690

A continuation criterion for the Landau equation with very soft and Coulomb potentials

Stanley Snelson·Caleb Solomon
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Abstract

We consider the spatially inhomogeneous Landau equation in the case of very soft and Coulomb potentials, $\gamma \in [-3,-2]$. We show that solutions can be continued as long as the following three quantities remain finite, uniformly in $t$ and $x$: (1) the mass density, (2) the velocity moment of order $s$ for any small $s>0$, and (3) the $L^p_v$ norm for any $p>3/(5+\gamma)$. In particular, we do not require a bound on the energy density.

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Stanley Snelson, Caleb Solomon. 2023-09-27. A continuation criterion for the Landau equation with very soft and Coulomb potentials. https://arxiv.org/abs/2309.15690

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