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

摘要: We show that the Lp spatial–temporal decay rates of solutions incompressible flow in an 2D exterior domain. When a domain has boundary, pressure term makes obstacle since we do not have enough information on near boundary. To overcome difficulty, adopt ideas He, Xin [C. Z. Xin, Weighted estimates for nonstationary Navier–Stokes equations domain, Methods Appl. Anal. 7 (3) (2000) 443–458], and our previous results [H.-O. Bae, B.J. Jin, Asymptotic behavior Stokes domains, J. Math. Fluid Mech., press; H.-O. Temporal spatial submitted publication]. For rate estimate, first extend temporal result general space when initial velocity is Lσ2∩Lr, 1