{"paper":{"title":"Quasi-geostrophic equation in $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Chunyou Sun, Maria B. Kania, Tomasz Dlotko","submitted_at":"2014-11-05T08:04:26Z","abstract_excerpt":"Solvability of Cauchy's problem in $\\mathbb{R}^2$ for subcritical quasi-geostrophic equation is discussed here in two phase spaces; $L^p(\\mathbb{R}^2)$ with $p> \\frac{2}{2\\alpha-1}$ and $H^s(\\mathbb{R}^2)$ with $s>1$. A solution to that equation in critical case is obtained next as a limit of the $H^s$-solutions to subcritical equations when the exponent $\\alpha$ of $(-\\Delta)^\\alpha$ tends to $\\frac{1}{2}^+$. Such idea seems to be new in the literature. Existence of the global attractor in subcritical case is discussed in the paper. In section 7 we also discuss solvability of the critical pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1178","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"}