Applied Mathematics and Mechanics

, Volume 17, Issue 8, pp 729–739 | Cite as

Phragmen-Lindelöf alternative results for the initial boundary problem of stokes equation

  • Cai Chongxi
  • Lin Changhao


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 solution of the initial boundary problem must either grow exponentially or decay exponentially with axial distance from the end of a semi-infinite strip. For the case of decay, we also establish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.

Key words

Stokes equation initial boundary problem phragmén-Lindelöf alternative theorem estimate of energy dissipation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. A.Ames and L. E.Payne, Decay estimates in steady pipe flow, SIAM J. Math. Anal., 20 (1986), 789.Google Scholar
  2. [2]
    W. S.Edelstein, A spatial decay estimates for the heat equation, J. Appl. Math. Phys., (ZAMP), 20 (1969), 900.Google Scholar
  3. [3]
    C. O.Horgan and J. K.Knowles, Recent developments concerning Saint-Veant's principle, in Advances in Applied Mechanics, ed. by T. Y.Wu and J. W.Hutchinson, Academic Press, San Diego, 23 (1983).Google Scholar
  4. [4]
    C. O.Horgan, Recent developments concerning Saint-Venant's principle: An Update Applied Mechanics Reviews, 42 (1989), 295.Google Scholar
  5. [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.Google Scholar
  6. [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.Google Scholar
  7. [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.Google Scholar
  8. [8]
    LinChanghao and L. E.Payne, Phragmén-Lindelöf type results for second order quasilinear parabolic equation in R 2, Z. Angew Math. Phys., 45 (1994), 294.Google Scholar
  9. [9]
    LinChanghao, Spatial decay estimates and energy bounds for the Stokes flow equation, SAACM, 2 (1992), 249.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Cai Chongxi
    • 1
  • Lin Changhao
    • 2
  1. 1.Zhongshan UniversityGuangzhouP. R. China
  2. 2.South China Normal UniversityGuangzhouP. R. China

Personalised recommendations