{"paper":{"title":"Large-data $L^2$-decay for attractive-dissipative nonlinear Schr\\\"odinger equations without the strong dissipative condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hayato Miyazaki, Naoyasu Kita, Takuya Sato","submitted_at":"2026-05-15T10:52:12Z","abstract_excerpt":"We prove a large-data $L^2$-decay estimate for nonlinear dissipative Schr\\\"odinger equations with attractive-dissipative power nonlinearity. The main difficulty is the lack of sign definiteness of the standard energy when $\\Re\\lambda<0$, which prevents the usual energy argument from directly yielding a uniform gradient bound. We introduce an augmented energy, obtained by adding a suitable multiple of the decreasing $L^2$-norm to the standard energy. This produces an additional dissipative term and gives a direct uniform-in-time $H^1$ bound without the iteration argument used in previous works."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15837","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15837/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.716120Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.849530Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fab5792c5e9095699440424b81822b1676218491fb7f208d3e2e9f769e4ce799"},"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"}