Asymptotic behavior for the Navier–Stokes equations in 2D exterior domains |
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Authors: | Hyeong-Ohk Bae Bum Ja Jin |
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Institution: | aDepartment of Mathematics, Ajou University, Suwon 443-749, Republic of Korea;bKorea Science Academy, Busanjin-Gu, Busan-Si, Republic of Korea |
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Abstract: | We show that the Lp 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 , 1<r q<∞ (1<r<q=∞). |
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Keywords: | 2D Navier– Stokes Temporal– spatial decay rate Exterior domain |
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