{"paper":{"title":"Finite time blow-up for the hypodissipative Navier Stokes equations with a force in $L^1_t C_x^{1,\\epsilon}\\cap L^{\\infty}_{t}L_{x}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego C\\'ordoba, Fan Zheng, Luis Mart\\'inez-Zoroa","submitted_at":"2024-07-09T11:47:27Z","abstract_excerpt":"In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $|\\nabla|^{\\alpha}$ for any $\\alpha\\in [0, \\alpha_0)$ ($\\alpha_0 = \\frac{22-8\\sqrt7}{9} > 0$). We construct solutions in $\\mathbb{R}^3\\times [0,T]$ with a finite $T>0$ and with an external forcing which is in $L^1_t([0, T]) C_x^{1,\\epsilon}\\cap L^{\\infty}_{t}L_{x}^2$, such that on the time interval $0 \\le t < T$, the velocity $u$ is in the space $C^\\infty\\cap L^2$ and such that as the time $t$ approaches the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06776","kind":"arxiv","version":2},"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/2407.06776/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"}