Phragmén-Lindel-f and Continuous Dependence Type Results in a Stokes Flow
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摘要: 就三维半无限柱体上的Stokes流动,研究边端效应的渐近性质.柱体水平面上的速度满足均匀的Dirichlet条件时,发现问题的解,随柱体有限端的距离,或呈指数增长,或呈指数衰减.最后讨论了方程参数的摄动影响.
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关键词:
- Phragmén-Lindel-f /
- 连续相关性 /
- 衰减范围 /
- Stokes流动
Abstract: The asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder was investigated. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, it is shown that solutions either grow exponentially or decay exponentially in the distance from the finite end of the cylinder. In the latter case the effect of perturbing the equation parameters is also investigated.-
Key words:
- Phragmén-Lindel-f /
- continuous dependence /
- decay bounds /
- Stokes flow
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[1] Ansorge R. Mathematical Models of Fluiddynamics[M]. Weinheim: Wiley-VCH, 2003:118. [2] LIN Chang-hao, Payne L E. The influence of domain and diffusivity perturbations on the decay end effects in heat conduction[J]. SIAM J Math Anal, 1994, 25(5): 1241-1258. doi: 10.1137/S003614109223355X [3] LIN Chang-hao, Payne L E. Phragmén-Lindelf type results for second order quasilinear parabolic equation in R2[J]. Z Angew Math Phys, 1994, 45(2): 294-311. doi: 10.1007/BF00943507 [4] LIN Chang-hao, Payne L E. A Phragmén-Lindelf alternative for a class of quasilinear second order parabolic problems[J]. Differential and Integral Equations, 1995, 8(3): 539-551. [5] Flavin J N, Knops R J, Payne L E. Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder[J]. Z Angew Math Phys, 1992, 43(3): 405-421. doi: 10.1007/BF00946237 [6] Horgan C O, Payne L E. Phragmén-Lindelf type results for harmonic functions with nonlinear boundary conditions[J]. Arch Rational Mech Anal, 1993, 122(2): 123-144. doi: 10.1007/BF00378164 [7] Payne L E, Song J C. Phragmén-Lindelf and continuous dependence type results in generalized heat conduction[J]. Z Angew Math Phys, 1996, 47(4): 527-538. doi: 10.1007/BF00914869 [8] Horgan C O. Recent developments concerning Saint-Venant’s principle: an update[J]. Appl Mech Rev, 1989, 42: 295-303. doi: 10.1115/1.3152414 [9] Horgan C O. Recent developments concerning Saint-Venant’s principle: a second update[J]. Appl Mech Rev, 1996, 49: 101-111. doi: 10.1115/1.3101961 [10] Horgan C O, Knowles J K. Recent developments concerning Saint-Venant’s principle[C]Hutchinson J W. Advances in Applied Mechanics. New York: Academic Press, Vol 23, 1983:179. [11] LIN Chang-hao. Spatial decay estimates and energy bounds for the Stokes flow equation[J]. SAACM, 1992, 2(3): 249-262. [12] LIN Chang-hao, Payne L E. Spatial decay bounds in the channel flow of an incompressible viscous fluid[J]. Mathematical Models & Methods in Applied Sciences, 2004, 14(6): 795-818. [13] 宋 J C. 平面Stokes流动中改良的空间衰减限[J]. 应用数学和力学, 2009, 30(7): 777-782. [14] Horgan C O, Wheeler L T. Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow[J]. SIAM J Appl Math, 1978, 35(1): 97-116. doi: 10.1137/0135008 [15] Song J C. Decay estimates for steady magnetohydrodynamic pipe flow[J]. Nonlinear Analysis, 2003, 54(6): 1029-1044. doi: 10.1016/S0362-546X(03)00124-X
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