{"paper":{"title":"Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hwa Kil Kim","submitted_at":"2012-06-12T21:00:00Z","abstract_excerpt":"In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let $H$ be a given Hamiltonian satisfying certain properties. We regularize $H$ using the Moreau-Yosida approximation and denote it by $H_\\tau.$ We show that solutions of the Hamiltonian system for $H_\\tau$ converge to a solution of the Hamiltonian system for $H$ as $\\tau$ converges to zero.\n  We provide sufficient conditions on $H$ to carry out this process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2673","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"}