{"paper":{"title":"A new formulation for the 3-D Euler equations with an application to subsonic flows in a cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shangkun Weng","submitted_at":"2012-12-07T15:50:46Z","abstract_excerpt":"In this paper, a new formulation for the three dimensional Euler equations is derived. Since the Euler system is hyperbolic-elliptic coupled in a subsonic region, so an effective decoupling of the hyperbolic and elliptic modes is essential for any development of the theory. The key idea in our formulation is to use the Bernoulli's law to reduce the dimension of the velocity field by defining new variables $(1,\\beta_2=\\frac{u_2}{u_1},\\beta_3=\\frac{u_3}{u_1})$ and replacing $u_1$ by the Bernoulli's function $B$ through $u_1^2=\\frac{2(B-h(\\rho))}{1+\\beta_2^2+\\beta_3^2}$. We find a conserved quant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1635","kind":"arxiv","version":3},"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"}