{"paper":{"title":"Blowup of $H^1$ solutions for a class of the focusing inhomogeneous nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2017-11-22T21:51:19Z","abstract_excerpt":"In this paper, we consider a class of the focusing inhomogeneous nonlinear Schr\\\"odinger equation \\[ i\\partial_t u + \\Delta u + |x|^{-b} |u|^\\alpha u = 0, \\quad u(0)=u_0 \\in H^1(\\mathbb{R}^d), \\] with $0<b<\\min\\{2,d\\}$ and $\\alpha_\\star\\leq \\alpha <\\alpha^\\star$ where $\\alpha_\\star =\\frac{4-2b}{d}$ and $\\alpha^\\star=\\frac{4-2b}{d-2}$ if $d\\geq 3$ and $\\alpha^\\star = \\infty$ if $d=1,2$. In the mass-critical case $\\alpha=\\alpha_\\star$, we prove that if $u_0$ has negative energy and satisfies either $xu_0 \\in L^2$ with $d\\geq 1$ or $u_0$ is radial with $d\\geq 2$, then the corresponding solution b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09088","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"}