Cai Chongxi, Lin Changhao. Phragmén-Lindelöf Alternative Results for the Initial Boundary Problem of Stokes Equation[J]. Applied Mathematics and Mechanics, 1996, 17(8): 689-698.
Citation: Cai Chongxi, Lin Changhao. Phragmén-Lindelöf Alternative Results for the Initial Boundary Problem of Stokes Equation[J]. Applied Mathematics and Mechanics, 1996, 17(8): 689-698.

Phragmén-Lindelöf Alternative Results for the Initial Boundary Problem of Stokes Equation

  • Received Date: 1995-05-17
  • Publish Date: 1996-08-15
  • 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.
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  • [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.
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