{"paper":{"title":"Wellposedness of the discontinuous ODE associated with two-phase flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","physics.flu-dyn"],"primary_cat":"math.CA","authors_text":"Dieter Bothe","submitted_at":"2019-05-11T17:50:08Z","abstract_excerpt":"We consider the initial value problem \\[ \\dot x (t) = v(t,x(t)) \\;\\mbox{ for } t\\in (a,b), \\;\\; x(t_0)=x_0 \\] which determines the pathlines of a two-phase flow, i.e.\\ $v=v(t,x)$ is a given velocity field of the type \\[ v(t,x)= \\begin{cases} v^+(t,x) &\\text{ if } x \\in \\Omega^+(t)\\\\ v^-(t,x) &\\text{ if } x \\in \\Omega^-(t) \\end{cases} \\] with $\\Omega^\\pm (t)$ denoting the bulk phases of the two-phase fluid system under consideration. The bulk phases are separated by a moving and deforming interface $\\Sigma (t)$. Since we allow for flows with phase change, these pathlines are allowed to cross or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04560","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"}