{"paper":{"title":"Morawetz estimates and spacetime bounds for quasilinear Schr\\\"{o}dinger equations with critical Sobolev exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Xianfa Song","submitted_at":"2019-04-22T02:46:21Z","abstract_excerpt":"In this paper, we study the following Cauchy problem \\begin{equation*} \\left\\{ \\begin{array}{lll} iu_t=\\Delta u + 2uh'(|u|^2)\\Delta h(|u|^2) + F(|u|^2)u\\mp A[h(|u|^2]^{2^*-1} h'(|u|^2)u,\\ x\\in \\mathbb{R}^N, \\ t>0\\\\ u(x,0)=u_0(x), \\quad x\\in \\mathbb{R}^N. \\end{array}\\right. \\end{equation*} Here $h(s)$ and $F(s)$ are some real-valued functions, $h(s)\\geq 0$ and $h'(s)\\geq 0$ for $s\\geq 0$, $N\\geq 3$, $A>0$. Besides obtaining sufficient conditions on the blowup in finite time and global existence of the solution, we establish Morawetz estimates and spacetime bounds for the global solution based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09702","kind":"arxiv","version":1},"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"}