{"id":"W2334639434","doi":"10.3934/cpaa.2012.11.1809","title":"On the Lagrangian averaged Euler equations: local well-posednessand blow-up criterion","year":2012,"lang":"en","type":"article","venue":"Communications on Pure &amp Applied Analysis","topic":"Navier-Stokes equation solutions","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; University of Alberta","keywords":"Euler equations; Mathematics; Lagrangian; Mathematical analysis; Lebesgue integration; Type (biology); Function (biology); Lagrangian and Eulerian specification of the flow field; Semi-implicit Euler method; Backward Euler method; Applied mathematics; Geology","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001238522,0.001011929,0.0008246149,0.001217162,0.000709991,0.001122893,0.0005036691,0.000921564,0.001934425],"category_scores_gemma":[0.002455717,0.0002785391,0.0007220684,0.0003419717,0.00160202,0.002778094,0.002451326,0.001368555,0.0001455022],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008272613,"about_ca_system_score_gemma":0.0006381962,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001104789,"about_ca_topic_score_gemma":0.001157808,"domain_scores_codex":[0.9997204,0.0000690333,0.00001960906,0.00006967893,0.00007382224,0.00004739371],"domain_scores_gemma":[0.9990011,0.0002897787,0.0002145438,0.00004801311,0.0002603172,0.0001861619],"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":[0.0001385089,0.00006007875,0.00395761,0.0004859387,0.0000942374,0.001023861,0.0005011666,0.1149299,0.04845912,0.8135154,0.001414767,0.01541929],"study_design_scores_gemma":[0.00001872511,0.0001435668,0.003113882,0.00009038786,0.00004884404,0.000462046,0.0002929029,0.7217939,0.008894937,0.2625075,0.002578755,0.00005455155],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4068133,0.004721958,0.5643198,0.002345667,0.0001657859,0.00008336749,0.0002671015,0.000205121,0.02107777],"genre_scores_gemma":[0.9566438,0.001368228,0.03287436,0.0001858292,0.0001387939,0.0001013343,0.0002036455,0.00008402406,0.008400015],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.001934425,"threshold_uncertainty_score":0.006550014,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1031882724239614,"score_gpt":0.3487402308718446,"score_spread":0.2455519584478831,"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."}}