{"paper":{"title":"Dynamical aspects of generalized Schr{\\\"o}dinger problem via Otto calculus -- A heuristic point of view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian L\\'eonard (MODAL'X), Ivan Gentil (ICJ), Luigia Ripani (ICJ)","submitted_at":"2018-06-05T08:29:54Z","abstract_excerpt":"The defining equation $(\\ast):\\  \\dot \\omega\\_t=-F'(\\omega\\_t),$ of a gradient flow is kinetic in essence. This article explores some dynamical (rather than kinetic) features of gradient flows  (i) by embedding equation $(\\ast)$ into the family of slowed down gradient flow equations: $\\dot \\omega ^{  \\varepsilon}\\_t=- \\varepsilon F'( \\omega ^{ \\varepsilon}\\_t),$ where $\\varepsilon>0$, and (ii) by considering   the \\emph{accelerations} $\\ddot \\omega ^{ \\varepsilon}\\_t$. We shall focus on Wasserstein gradient flows. Our approach is mainly heuristic. It relies on Otto calculus.A special formulati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01553","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"}