{"paper":{"title":"Eulerian dynamics with a commutator forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eitan Tadmor, Roman Shvydkoy","submitted_at":"2016-12-13T17:33:33Z","abstract_excerpt":"We study a general class of Euler equations driven by a forcing with a \\emph{commutator structure} of the form $[\\mathcal{L},\\mathbf{u}](\\rho)=\\mathcal{L}(\\rho \\mathbf{u})- \\mathcal{L}(\\rho)\\mathbf{u}$, where $\\mathbf{u}$ is the velocity field and $\\mathcal{L}$ is the \"action\" which belongs to a rather general class of translation invariant operators. Such systems arise, for example, as the hydrodynamic description of velocity alignment, where action involves convolutions with bounded, positive influence kernels, $\\mathcal{L}_\\phi(f)=\\phi*f$. Our interest lies with a much larger class of $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04297","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"}