{"paper":{"title":"H\\\"{o}lder continuous weak solution of 2d Boussinesq equation with diffusive temperature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liqun Zhang, Tao Tao, Tianwen Luo","submitted_at":"2019-01-29T02:25:42Z","abstract_excerpt":"We show the existence of H\\\"{o}lder continuous periodic weak solutions of the 2d Boussinesq equation with diffusive temperature which satisfy the prescribed kinetic energy. More precisely, for any smooth $e(t):[0,1]\\rightarrow R_+$ and $\\varepsilon\\in (0, \\frac{1}{10})$, there exist $v\\in C^{\\frac{1}{10}-\\varepsilon}([0,1]\\times {\\rm T}^2), \\theta\\in C_t^{1,\\frac{1}{20}-\\frac{\\varepsilon}{2}}C_x^{2,\\frac{1}{10}-\\varepsilon}([0,1]\\times {\\rm T}^2)$ which solve boussinesq equation in the sense of distribution and satisfy e(t)=\\int_{{\\rm T}^2}|v(t,x)|^2dx, \\quad \\forall t\\in [0,1]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10071","kind":"arxiv","version":3},"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"}