{"paper":{"title":"Global in Time Estimates for the Spatially Homogeneous Landau Equation with Soft Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kung-Chien Wu","submitted_at":"2013-06-05T19:51:58Z","abstract_excerpt":"This paper deals with some global in time a priori estimates of the spatially homogeneous Landau equation for soft potentials $\\ga\\in[-2,0)$. For the first result, we obtain the estimate of weak solutions in $L^{\\alpha}_{t}L_{v}^{3-\\eps}$ for $\\alpha=\\frac{2(3-\\eps)}{3(2-\\eps)}$ and $0<\\eps<1$, which is an improvement over estimates by Fournier-Guerin [N. Fournier; H. Guerin, Well-posedness of the spatially homogeneous Landau equation for soft potentials. J. Funct. Anal. 25(2009), no. 8, 2542--2560]. Foe the second result, we have the estimate of weak solutions in $L_{t}^{\\infty}L^{p}_{v}$, $p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1220","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}