{"id":73,"date":"2020-02-09T19:00:00","date_gmt":"2020-02-09T18:00:00","guid":{"rendered":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/?p=73"},"modified":"2026-01-07T19:01:19","modified_gmt":"2026-01-07T18:01:19","slug":"global-regularity-estimates-for-the-boltzmann-equation","status":"publish","type":"post","link":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/2020\/02\/09\/global-regularity-estimates-for-the-boltzmann-equation\/","title":{"rendered":"Global regularity estimates for the Boltzmann equation"},"content":{"rendered":"\n<p>I wrote with <a href=\"http:\/\/www.math.uchicago.edu\/~luis\/\">Luis Silvestre<\/a> (<a href=\"http:\/\/www.math.uchicago.edu\/\">University of Chicago<\/a>) a series of articles about the Boltzmann equation without cut-off in the inhomogeneous case. The goal was to prove C<sup>\u221e<\/sup> a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to point-wise bounds on their mass, energy and entropy densities.<\/p>\n\n\n\n<p>The final paper is entitled <a href=\"https:\/\/arxiv.org\/abs\/1909.12729\">Global regularity estimates for the Boltzmann equation without cut-off<\/a>.<\/p>\n\n\n\n<p>It relies on the L<sup>\u221e<\/sup> estimate derived by Luis Silvestre (see <a href=\"https:\/\/arxiv.org\/abs\/1412.4706\">this paper<\/a>), the local H\u00f6lder estimate derived in <a href=\"https:\/\/arxiv.org\/abs\/1608.07571\">this paper<\/a>, the Schauder estimate for kinetic equations with integral diffusion derived in <a href=\"https:\/\/arxiv.org\/abs\/1812.11870\">this paper<\/a> and the pointwise decay estimates for large velocities derived in <a>this paper<\/a> with <a href=\"https:\/\/cmouhot.wordpress.com\/\">Cl\u00e9ment Mouhot<\/a> and Luis Silvestre.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I wrote with Luis Silvestre (University of Chicago) a series of articles about the Boltzmann equation without cut-off in the inhomogeneous case. The goal was to prove C\u221e a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to point-wise bounds on their mass, energy and entropy densities. The final paper is [&hellip;]<\/p>\n","protected":false},"author":138,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-73","post","type-post","status-publish","format-standard","hentry","category-preprint"],"_links":{"self":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/73","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/users\/138"}],"replies":[{"embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/comments?post=73"}],"version-history":[{"count":1,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/73\/revisions"}],"predecessor-version":[{"id":74,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/73\/revisions\/74"}],"wp:attachment":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/media?parent=73"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/categories?post=73"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/tags?post=73"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}