{"paper":{"title":"Some free boundary problem for two phase inhomogeneous incompressible flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hirokazu Saito, Xin Zhang, Yoshihiro Shibata","submitted_at":"2018-11-06T06:15:16Z","abstract_excerpt":"In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous flows with moving interfaces in $L_p-L_q$ maximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by Y.Shibata \\& S.Shimizu, we find the local solutions in $L_p-L_q$ class in some general uniform $W^{2-1\\slash r}_r$ domain in $\\BBR^N$ by assuming $(p, q)\\in ]2,\\infty[\\times ]N,\\infty[$ or $(p, q)\\in ]1,2[ \\times ]N,\\infty[$ satisfying $1 \\slash p + N \\slash q>3\\slash 2.$ In particular, less regular initial data are allowed by assuming $p<2.$ In addition, if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02179","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"}