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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 9
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Original Articles

A time-dependent perturbation solution from a steady state for Marangoni problem

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Pages 1526-1539 | Received 28 Sep 2016, Accepted 04 Apr 2017, Published online: 17 Apr 2017

References

  • Abidin NZ , Arifin NM , Noorani MSM . Boundary effect on Marangoni convection in a variable viscosity fluid layer. J Math Stat. 2008;4(1):1–8.
  • Guo ZL , Lin P , Wang YF . Continuous finite element schemes for a phase field model in two-layer fluid Bénard–Marangoni convection computations. Comput Phys Commun. 2014;185(1):63–78.
  • Pedlosky J . Geophysical fluid dynamics. New York (NY): Springer-Verlag; 1987.
  • Pardo R , Herrero H , Hoyas S . Theoretical study of a Bénard–Marangoni problem. J Math Anal Appl. 2011;376(1):231–246.
  • Peterson JW , Carey GF . Parallel adaptive solution of coupled Rayleigh–Bénard–Marangoni problems with the Navier-slip. Int J Numer Methods Fluids. 2011;66(4):428–451.
  • Ma T , Wang SH . Rayleigh–Bénard convection: dynamics and structure in the physical space. Commun Math Sci. 2007;5(3):553–574.
  • Pearson JRA . On convection cells induced by surface tension. J Fluid Mech. 1958;4:489–500.
  • Shivakumara IS , Venkatachalappa M , Suma SP . Exact analysis of Marangoni convection with throughflow. Acta Mech. 1999;136:109–117.
  • Lorca SA , Boldrini JL . Stationary solutions for generalized Boussinesq models. J Differ Equ. 1996;124:389–406.
  • Lorca SA , Boldrini JL . The initial value problem for a generalized Boussinesq model. Nonlinear Anal. 1999;36(4):457–480.
  • Ōeda K . On the initial value problem for the heat convection equation of Boussinesq approximation in a time-dependent domain. Proc Jpn Acad, Ser A. 1988;64(5):143–146.
  • Ōeda K . Weak and strong solutions of the heat convection equations in regions with moving boundaries. J Fac Sci Univ Tokyo, Sec IA. 1989;36:491–536.
  • Rabinowitz PH . Existence and nonuniqueness of rectangular solutions of the Bénard problem. Arch Ration Mech Anal. 1968;29:32–57.
  • Rabinowitz PH . Some global results for nonlinear eigenvalue problems. J Funct Anal. 1971;7:487–513.
  • Nishida T , Teramoto Y . Bifurcation theorems for the model system of Bénard–Marangoni convection. J Math Fluid Mech. 2009;11(3):383–406.
  • Hoyas S , Fajardo P , Gil A , et al . Analysis of bifurcations in a Bénard–Marangoni problem: gravitational effects. Int J Heat Mass Transfer. 2014;73:33–41.
  • Hou TY , Li CM . Global well-posedness of the viscous Boussinesq equations. Discrete Contin Dyn Syst. 2005;12(1):1–12.
  • Hsia CH , Ma T , Wang SH . Rotating Boussinesq equations: dynamic stability and transitions. Discrete Contin Dyn Syst. 2010;28:99–130.
  • Hmidi T , Keraani S , Rousset F . Global well-posedness for a Boussinesq–Navier–Stokes system with critical dissipation. J Differ Equ. 2010;249(9):2147–2174.
  • Ma T . Theory and method of partial differential equation. Beijing: Science Press; 2011. Chinese.
  • Ma T , Wang SH . Phase transition dynamics in nonlinear science. Springer-Verlag; 2013, 636pp.
  • Teman R . Navier–Stokes equations. Theory and numerical analysis. Reprint of the 1984 edition. Providence (RI): AMS Chelsea Publishing; 2001.
  • Teman R . Infinite-dimensional dynamical systems in mechanics and physics. 2nd ed. New York (NY): Springer-Verlag; 1997. 648 pp.
  • Gilbarg D , Trudinger NS . Elleptic partial differential equations of second order. New York (NY): Springer; 1998.

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