{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:37:04Z","timestamp":1787319424117,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2018R1D1A1B06050386"],"award-info":[{"award-number":["2018R1D1A1B06050386"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We prove the global existence of cavity dynamics and regularity for the solutions of the Navier\u2013Stokes equations of compressible barotropic flows that have initially jump discontinuities along the curve grazing two nonconvex corners. Rectangular cavities may produce corner shear layers and jump discontinuities between lid and cavity interior. We construct a vector field lifting the jump values into the region and sort out the corner singularity functions by the Lam\u00e9 system with zero boundary condition. We show that the velocity vector has the decomposition into the lifting vector plus the corner singularity plus the remainder of the twice differentiability. The fluid density and velocity gradient have jump discontinuities across the curve as predicted by Rankine\u2013Hugoniot conditions. The interface curve remains [Formula: see text], [Formula: see text], despite the singular decomposition of the velocity vector.<\/jats:p>","DOI":"10.1137\/22m152270x","type":"journal-article","created":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T10:23:51Z","timestamp":1695378231000},"page":"4599-4639","source":"Crossref","is-referenced-by-count":1,"title":["Cavity Dynamics and Regularity for Compressible Navier\u2013Stokes Equations"],"prefix":"10.1137","volume":"55","author":[{"given":"Jae Ryong","family":"Kweon","sequence":"first","affiliation":[{"name":"Department of Mathematics, POSTECH, Pohang 790\u2013784, Kyoungbuk, Republic of Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,9,22]]},"reference":[{"key":"ref1","volume-title":"Sobolev Spaces","author":"Adams R. A.","year":"1975"},{"key":"ref2","volume-title":"Fundamentals of Aerodynamics","author":"Anderson J. 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