{"id":"W2952329349","doi":"10.48550/arxiv.1307.7090","title":"Strong Ill-posedness of the incompressible Euler equation in borderline Sobolev spaces","year":2013,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Navier-Stokes equation solutions","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Sobolev space; Norm (philosophy); Compressibility; Euler's formula; Mathematics; Mathematical analysis; Euler equations; Euler system; Space (punctuation); Pure mathematics; Mathematical physics; Physics; Computer science; Law","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003981114,0.0002957828,0.0004561032,0.0003247739,0.0001225143,0.00004230066,0.0008780633,0.0003431592,0.0002066228],"category_scores_gemma":[0.0003913533,0.0002767212,0.0002142032,0.0007005843,0.0002031618,0.0002659148,0.00102999,0.0006635088,0.00004404036],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002978662,"about_ca_system_score_gemma":0.0002733154,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006552864,"about_ca_topic_score_gemma":0.0005005572,"domain_scores_codex":[0.9981723,0.0003426857,0.0004685757,0.0005295402,0.0001902308,0.0002967055],"domain_scores_gemma":[0.9971247,0.0004734932,0.0007678715,0.001136633,0.0004242869,0.00007299088],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00004092104,0.0005506081,0.01985355,0.0005231852,0.0001586196,0.0000103315,0.001327128,0.3563267,0.0003273405,0.6197096,0.0008527876,0.0003193069],"study_design_scores_gemma":[0.001781486,0.00003836022,0.009966886,0.0009097369,0.0003356003,0.000001326607,0.001420223,0.5141992,0.0009051519,0.4691873,0.0005265966,0.0007281904],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8845242,0.0000658291,0.1102087,0.0001955488,0.0005509358,0.000876837,0.00005257893,0.00007954632,0.003445811],"genre_scores_gemma":[0.9958146,0.0000509586,0.001425253,0.00001859834,0.00005622915,0.000005547717,0.00002707155,0.00003373078,0.002568073],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1578725,"threshold_uncertainty_score":0.9999685,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1910556368195408,"score_gpt":0.2582117198872438,"score_spread":0.06715608306770296,"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."}}