{"paper":{"title":"Stability of isentropic viscous shock profiles in the high-Mach number limit","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey Humpherys, Kevin Zumbrun, Olivier Laffite","submitted_at":"2007-05-29T15:58:18Z","abstract_excerpt":"By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier--Stokes equations with $\\gamma$-law pressure (i) in the limit as Mach number $M$ goes to infinity, for any $\\gamma\\ge 1$ (proved analytically), and (ii) for $M\\ge 2,500$, $\\gamma\\in [1,2.5]$ (demonstrated numerically). This builds on and completes earlier studies by Matsumura--Nishihara and Barker--Humpherys--Rudd--Zumbrun establishing stability for low and intermediate Mach numbers, respectively, indicating unconditiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4244","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":""},"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"}