{"id":56,"date":"2023-12-18T18:19:00","date_gmt":"2023-12-18T17:19:00","guid":{"rendered":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/?p=56"},"modified":"2026-01-07T18:20:57","modified_gmt":"2026-01-07T17:20:57","slug":"partial-regularity-for-the-boltzmann-equation","status":"publish","type":"post","link":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/2023\/12\/18\/partial-regularity-for-the-boltzmann-equation\/","title":{"rendered":"Partial regularity for the Boltzmann equation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center\">The case of very soft potentials<\/h2>\n\n\n\n<p>With <a href=\"https:\/\/www.cmls.polytechnique.fr\/perso\/golse\/\">F. Golse<\/a>  and <a href=\"https:\/\/math.uchicago.edu\/~luis\/\">Luis Silvestre<\/a>, we uploaded a new paper entitled: <em>Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials<\/em>. <a href=\"https:\/\/hal.science\/hal-04349073\">HAL<\/a> | <a href=\"https:\/\/arxiv.org\/abs\/2312.11079\" target=\"_blank\" rel=\"noreferrer noopener\">arxiv<\/a><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"497\" src=\"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/non-deg-sphere-1024x497.png\" alt=\"\" class=\"wp-image-33\" srcset=\"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/non-deg-sphere-1024x497.png 1024w, https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/non-deg-sphere-300x145.png 300w, https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/non-deg-sphere-768x372.png 768w, https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-content\/uploads\/sites\/93\/2026\/01\/non-deg-sphere.png 1233w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>Summary:<\/strong> <em>We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials constructed as in Villani (1998) has Hausdorff dimension at most |\u03b3+2s|\/2s with \u03b3\u2208[\u22124s,\u22122s) and s\u2208(0,1). <\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The case of very soft potentials With F. Golse and Luis Silvestre, we uploaded a new paper entitled: Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials. HAL | arxiv Summary: We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials [&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-56","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\/56","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=56"}],"version-history":[{"count":3,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/56\/revisions"}],"predecessor-version":[{"id":59,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/posts\/56\/revisions\/59"}],"wp:attachment":[{"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/media?parent=56"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/categories?post=56"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/perso.imj-prg.fr\/cyril-imbert\/wp-json\/wp\/v2\/tags?post=56"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}