{"paper":{"title":"Growth of Sobolev norms in the cubic defocusing nonlinear Schr\\\"odinger equation with a convolution potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Marcel Guardia","submitted_at":"2012-11-06T15:35:49Z","abstract_excerpt":"Fix $s>1$. Colliander, Keel, Staffilani, Tao and Takaoka proved in \\cite{CollianderKSTT10} the existence of solutions of the cubic defocusing nonlinear Schr\\\"odinger equation in the two torus with $s$-Sobolev norm growing in time. In this paper we generalize their result to the cubic defocusing nonlinear Schr\\\"odinger equation with a convolution potential. Moreover, we show that the speed of growth is the same as the one obtained for the cubic defocusing nonlinear Schr\\\"odinger equation in \\cite{GuardiaK12}. The results we obtain can deal with any potential in $H^{s_0}(\\TT^2)$, $s_0>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1267","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"}