{"paper":{"title":"Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","nlin.CD","physics.ao-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Divakar Viswanath, Y. Charles Li","submitted_at":"2008-11-03T20:28:40Z","abstract_excerpt":"We derive necessary conditions that traveling wave solutions of the Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution irrespective of the Reynolds number ($Re$). Other conditions are asymptotic in the limit $Re\\to\\infty$. The exact conditions are likely to be useful tools in the study of transitional structures. For the pipe flow geometry, we give computations up to $Re=100000$ showing the connection of our asymptotic conditions to critical layers that accompany vortex structures at hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0383","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":""},"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"}