Asymptotic behavior for the Navier-Stokes equations in 2D exterior domains

摘要

We show that the L-p spatial-temporal decay rates of solutions of incompressible flow in an 2D exterior domain. When a domain has a boundary, pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary. To overcome the difficulty, we adopt the ideas in He, Xin [C. He, Z. Xin, Weighted estimates for nonstationary Navier-Stokes equations in exterior domain, Methods Appl. Anal. 7 (3) (2000) 443-458], and our previous results [H.-O. Bae, B.J. Jin, Asymptotic behavior of Stokes solutions in 2D exterior domains, J. Math. Fluid Mech., in press; H-O. Bae, B.J. Jin, Temporal and spatial decay rates of Navier-Stokes solutions in exterior domains, submitted for publication]. For the spatial decay rate estimate, we first extend temporal decay rate result of the Navier-Stokes solutions for general LP space when the initial velocity is in L-sigma(2) boolean AND L-r, 1 < r <= q < infinity (1 < r < q = infinity). (C) 2006 Elsevier Inc. All rights reserved.