This paper is a continuation work of[26]and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow.We assume the initial dens...This paper is a continuation work of[26]and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow.We assume the initial densityρ0=η11Ω0+η21Ω0^c,where(η1,η2)is any pair of positive constants andΩ0 is a bounded,simply connected domain with W^k+2,p(R^2)boundary regularity.We prove that for any positive time t,the density functionρ(t)=η11Ω(t)+η21Ω(t)^c,and the domainΩ(t)preserves the W^k+2,p-boundary regularity.展开更多
基金MCM for the hospitality and the financial supportsupported by SFB 1060+2 种基金Universitat Bonn during the last part of the workpartially supported by NSF of China under Grants Nos.11371347 and 11688101innovation grant from National Center for Mathematics and Interdisciplinary Sciences
文摘This paper is a continuation work of[26]and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow.We assume the initial densityρ0=η11Ω0+η21Ω0^c,where(η1,η2)is any pair of positive constants andΩ0 is a bounded,simply connected domain with W^k+2,p(R^2)boundary regularity.We prove that for any positive time t,the density functionρ(t)=η11Ω(t)+η21Ω(t)^c,and the domainΩ(t)preserves the W^k+2,p-boundary regularity.
