{"paper":{"title":"Well-posedness for stochastic scalar conservation laws on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Darko Mitrovic, Eduard Nigsch, Nikola Konatar","submitted_at":"2018-09-06T07:57:49Z","abstract_excerpt":"We consider the scalar conservation law with stochastic forcing $$ \\partial_t u +\\mathrm{div}_g {\\mathfrak f}(\\mx,u)= \\Phi(\\mx,u) dW, \\ \\ {\\bf x} \\in M, \\ \\ t\\geq 0 $$ on a smooth compact Riemannian manifold $(M,g)$ where $W$ is the Wiener process and ${\\bf x}\\mapsto {\\mathfrak f}(\\mx,\\xi)$ is a vector field on $M$ for each $\\xi\\in {\\bf R}$. We introduce admissibility conditions, derive the kinetic formulation and use it to prove well posedness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01866","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"}