Document Type
Article
Publication Date
11-1-2020
Abstract
We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform polynomial decay in the velocity variable, and that satisfies a technical lower bound assumption (but can have vacuum regions). For uniqueness in this weak class, we have to make the additional assumption that the initial data is Hölder continuous. Our hypotheses are much weaker, in terms of regularity and decay, than previous large-data well-posedness results in the literature. We also derive a continuation criterion for our solutions that is, for the case of very soft potentials, an improvement over the previous state of the art.
Publication Source (Journal or Book title)
Annales De L Institut Henri Poincare C Analyse Non Lineaire
First Page
1345
Last Page
1377
Recommended Citation
Henderson, C., Snelson, S., & Tarfulea, A. (2020). Local solutions of the Landau equation with rough, slowly decaying initial data. Annales De L Institut Henri Poincare C Analyse Non Lineaire, 37 (6), 1345-1377. https://doi.org/10.1016/j.anihpc.2020.04.004