Stoxes方程初边值问题的Phragmén-Lindelöf二择性原理*
Phragmén-Lindelöf Alternative Results for the Initial Boundary Problem of Stokes Equation
-
摘要: 本文对非定常的Stokes方程的初边值问题证明了Phragmén-Lindelöf二择性原理,即证明Stokes流函数的能量,随着与带状区域有限端距离的增加必定或者按指数率增长或者按指数率衰减.对能量衰减情况建立了Stokes流速度的最大模的点点估计.并提出求全能量上界的方法.
-
关键词:
- Stokes方程 /
- 初边值问题 /
- Phragmén-Lindelöf二择性原理 /
- 能量耗散估计
Abstract: In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation,i.e.we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentially wilh axial distance from the end of a semi-infinite strip.For the case of decay,we alsoestablish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy. -
[1] K.A.Ames and L.E.Payne,Decay estimates in steady pipe flow,SIAM J.Math.Anal.,20(1986),789. [2] W.S.Edelstein,A spatial decay estimates for the heat equation,J.Appl.Math.Phys.,(ZAMP) 20(1969),900. [3] C.O.Horgan and J.K.Knowles,Recent developments concerning Saint-Veant's principle,in Adrances in Applied Mechanics,ed.by T.Y.Wu and J.W.Hutchinson,Academic Press,San Diego,23(1983). [4] C.O.Horgan,Recent developments concerning Saint-Venant's principle:An Update Applied Mechanics Reviews,42(1989),295. [5] C.O.Horgan.Decay estimates for the biharmonic equation with application to Saint-Venant principle in plane elasticity and Stokes flows,Q.Appl.Math.,47(1989),147. [6] C.O.Horgan and L.E.Payne,Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions,Arch.Rational Mech.Anal.,122(1993),123. [7] C.O.Horgan and L.E.Payne,On the asymptotic behavior of solution of linear second order boundary problem on a semi-infinite strip,Arch.Rational Mech.Anal.,124(1993),277 [8] Lin Changhao and L.E.Payne,Phragmén-Lindelöf type results for seconn order quasilinear parabolic equation in R2,Z.Angew Math.Phys,45(1994),294. [9] Lin Changhao,Spatial decay estimates and energy bounds for the Stokes flow equation,SAACM,2(1992),249.
点击查看大图
计量
- 文章访问数: 2139
- HTML全文浏览量: 97
- PDF下载量: 436
- 被引次数: 0