{"id":"W2130044878","doi":"10.1016/j.jfa.2007.09.005","title":"A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order","year":2007,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":73,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Sobolev space; Mathematics; A priori and a posteriori; Norm (philosophy); Geodetic datum; Nonlinear system; Initial value problem; Mathematical analysis; Real line; Cauchy problem; A priori estimate; Physics; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.007112584,0.003440387,0.001622161,0.005525234,0.002004046,0.005341885,0.002398134,0.003737023,0.005749257],"category_scores_gemma":[0.02808395,0.001270932,0.001367957,0.001178598,0.005611193,0.01038991,0.00557474,0.007374924,0.000647166],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003001094,"about_ca_system_score_gemma":0.001507169,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002277313,"about_ca_topic_score_gemma":0.001905179,"domain_scores_codex":[0.9985655,0.0006882003,0.00009779326,0.0001484104,0.0003346477,0.0001654124],"domain_scores_gemma":[0.9739146,0.01815721,0.001894548,0.0006856999,0.002870593,0.002477421],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0002277973,0.00008769569,0.0006035995,0.0002101609,0.00004940435,0.0001929827,0.0004281737,0.009660282,0.006386311,0.9765704,0.001243668,0.004339614],"study_design_scores_gemma":[0.00003009785,0.0001064185,0.0008364043,0.0001107607,0.00003546768,0.0001650747,0.000259397,0.2177886,0.002070416,0.7768422,0.001674697,0.00008043648],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4403206,0.007606583,0.4677607,0.0123569,0.001068985,0.0001231378,0.0004674773,0.0004264567,0.06986905],"genre_scores_gemma":[0.8862182,0.004411873,0.06155267,0.001193984,0.001541273,0.0002628824,0.0007517137,0.0005065843,0.04356076],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007112584,"threshold_uncertainty_score":0.03761536,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07999637209533098,"score_gpt":0.3396217904565833,"score_spread":0.2596254183612523,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}