{"paper":{"title":"Existence of Weak Solutions to a Power-Law Model for Compressible Non-Newtonian Fluids on 1D Unbounded Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianing Yang, Siran Li, Yuantu Zhu","submitted_at":"2026-08-01T14:29:28Z","abstract_excerpt":"This paper is concerned with the analysis of a one-dimensional power-law model for compressible fluid dynamics on $\\mathbb{R}$, in which the shear stress takes the form $\\mu |\\partial_{x}u|^{p-2}\\partial_{x}u$, where $\\mu$ is the viscosity coefficient and $u$ is the velocity. We prove that, in the singular limit $p\\rightarrow\\infty$, the solutions converge to functions $(\\rho,u)$ satisfying $|\\partial_{x}u|\\leq 1$, $\\tau = \\pi \\partial_{x}u$, $\\pi \\geq 0$, and $\\pi (1 - |\\partial_{x}u|) = 0$ a.e. on $\\mathbb{R}$. Moreover, we rigorously justify the existence of weak solutions to the limiting e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00689","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/2608.00689/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"}