{"paper":{"title":"On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Axel Gruenrock","submitted_at":"2000-06-26T17:57:11Z","abstract_excerpt":"The Cauchy- and periodic boundary value problem for the nonlinear Schroedinger equations in $n$ space dimensions [u_t - i\\Delta u = (\\nabla \\bar{u})^{\\beta}, |\\beta|=m \\ge 2, u(0)=u_0 \\in H^{s+1}_x] is shown to be locally well posed for $s > s_c := \\frac{n}{2} - \\frac{1}{m-1}$, $s \\ge 0$. In the special case of space dimension $n=1$ a global $L^2$-result is obtained for NLS with the nonlinearity $N(u)= \\partial_x (\\bar{u} ^2)$.\n  The proof uses the Fourier restriction norm method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0006195","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/math/0006195/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}