{"paper":{"title":"Multiharmonic analysis for nonlinear acoustics with different scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adrien Semin, Anastasia Thoens-Zueva, Kersten Schmidt","submitted_at":"2017-01-09T09:06:39Z","abstract_excerpt":"The acoustic wave-propagation without mean flow and heat flux can be described in terms of velocity and pressure by the compressible nonlinear Navier-Stokes equations, where boundary layers appear at walls due to the viscosity and a frequency interaction appears, $\\textit{i.e.}$ sound at higher harmonics of the excited frequency $\\omega$ is generated due to nonlinear advection. We use the multiharmonic analysis to derive asymptotic expansions for small sound amplitudes and small viscosities both of order $\\varepsilon^2$ in which velocity and pressure fields are separated into far field and cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02097","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"}