{"paper":{"title":"The geometry of barotropic flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stephen C. Preston","submitted_at":"2013-02-20T19:00:31Z","abstract_excerpt":"In this article we write the equations of barotropic compressible fluid mechanics as a geodesic equation on an infinite-dimensional manifold. The equations are given by \\begin{align} u_t + \\nabla_uu = -\\frac{1}{\\rho} \\grad p \\\\ \\rho_t + \\diver{(\\rho u)} = 0, \\end{align} where the fluid fills up a compact manifold $M$, $u$ is a time-dependent velocity field on $M$, and $\\rho$ is the density, a positive function on $M$. The barotropic assumption is that the pressure $p$ is some given function of the density, although our methods also extend to certain more general isentropic flows. Our infinite-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5071","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"}