(untitled) (Analysis in Theory and Applications, 2019)
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 density ρ_0=η_11_Ω_0+η_21_Ω_0^c, where (η_1,η_2) is any pair of positive constants and Ω_0 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 function ρ(t)=η_11_Ω(t)+η_21_Ω(t)^c, and the domain Ω(t) preserves the W^k+2,p-boundary regularity.