{"paper":{"title":"Spatial asymptotic expansions in the incompressible Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peter Topalov, R. McOwen","submitted_at":"2016-06-26T17:34:10Z","abstract_excerpt":"In this paper we prove that the Euler equation describing the motion of an ideal fluid in $\\R^d$ is well-posed in a class of functions allowing spatial asymptotic expansions as $|x|\\to\\infty$ of any a priori given order. These asymptotic expansions can involve log terms and lead to a family of conservation laws. Typically, the solutions of the Euler equation with initial data in the Schwartz class develop non-trivial spatial asymptotic expansions of the type considered here."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08059","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"}