Decay estimates for strong solutions of the Navier-Stokes equations in exterior domains

被引:1
作者
Wiegner M. [1 ]
机构
[1] Department of Mathematics I, RWTH Aachen
来源
Annali dell’Università di Ferrara | 2000年 / 46卷 / 1期
关键词
Weak Solution; Strong Solution; Decay Estimate; Exterior Domain; Global Strong Solution;
D O I
10.1007/BF02837290
中图分类号
学科分类号
摘要
Based on the Lp-Lq-estimates for the Stokes semigroup on exterior domains, proven by Iwashita and refined by Maremonti-Solonnikov and Shibata, the precise time-asymptotic behaviour of solutions of the Navier-Stokes equations is derived. The estimates are improved, if some additional information on the initial value is available. The results apply also to weak solutions in three and four dimensions. © 2000 Università degli Studi di Ferrara.
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页码:61 / 79
页数:18
相关论文
共 14 条
  • [1] Amrouche C., Girault V., Schonbek M.E., Schonbek T.P., Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations
  • [2] Borchers W., Miyakawa T., Algebraic L<sup>2</sup>decay for Navier-Stokes flows in Exterior domains, Acta Math., 165, pp. 189-227, (1990)
  • [3] Borchers W., Miyakawa T., Algebraic L<sup>2</sup>decay for Navier-Stokes flows in Exterior domains II, Hiroshima Math. J., 21, pp. 621-640, (1991)
  • [4] Cannone M., Planchon F., Schonbek M.E., Strong solutions to the incompressible Navier-Stokes equations in the half-space
  • [5] Dan W., Kobayashi T., Shibata Y., On the local energy decay approach to some fluid flow in an exterior domain, Lecture Notes in Num. Appl. Anal., 16, pp. 1-51, (1998)
  • [6] Iwashita H., L<sub>q</sub>-L<sub>r</sub> Estimates for Solutions of Nonstationary Stokes Eqauation in an Exterior Domain and the Navier-Stokes Initial Value Problems in L<sub>q</sub> Spaces, Math. Ann., 285, pp. 265-288, (1989)
  • [7] Kozono H., Ogawa T., Sohr H., Asymptotic Behaviour in L<sup>n</sup>for Turbulent Solutions of the Navier-Stokes Equations in Exterior Domains, Manuscripta Math., 74, pp. 253-275, (1992)
  • [8] Maremonti P., Solonnikov V.A., On nonstationary Stokes problem in exterior domains, (1996)
  • [9] Schonbek M.E., Large-time behavior of solutions of the Navier-Stokes equations, Comm. P.D.E., 11, pp. 753-763, (1986)
  • [10] Wiegner M., Decay results for weak solutions of the Navier-Stokes equations in, London Math. Soc., 35, pp. 303-313, (1987)