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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.02179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-06T06:15:16Z","cross_cats_sorted":[],"title_canon_sha256":"5c9bb0c2e52dcdcfd72340be5755dac2d8d8543bf12872afef687e7251936099","abstract_canon_sha256":"c693b88498bb47040ce65f50c67d1fd02a8f4a5d4ce988c521e553238d941aa9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:24.874632Z","signature_b64":"uGDK6JxdcCMeWyfF1JK+BhITiAcwgy7SEAHxabdSgzaToCHoQiuyszJkIAEB07XFg2c+oLxTDC+uCZulhJ1/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f1d08fa5b7f5c8a81bb88233d4d0283ca9f823c5d0e550964ca4f31caab92d3","last_reissued_at":"2026-05-18T00:01:24.874246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:24.874246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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