{"paper":{"title":"On Stability of Pseudo-Conformal Blowup for L^2-critical Hartree NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Joachim Krieger, Pierre Raphael","submitted_at":"2008-08-18T00:39:50Z","abstract_excerpt":"We consider $L^2$-critical focusing nonlinear Schroedinger equations with Hartree type nonlinearity $$i \\pr_t u = -\\DD u - \\big (\\Phi \\ast |u|^2 \\big) u \\quad {in $\\RR^4$},$$ where $\\Phi(x)$ is a perturbation of the convolution kernel $|x|^{-2}$. Despite the lack of pseudo conformal invariance for this equation, we prove the existence of critical mass finite-time blowup solutions $u(t,x)$ that exhibit the pseudo-conformal blowup rate $$ \\| \\nabla u(t) \\|_{L^2_x} \\sim \\frac{1}{|t|} \\quad {as} \\quad t \\nearrow 0 . $$ Furthermore, we prove the finite-codimensional stability of this conformal blow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2324","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"}