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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 12
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Articles

Stabilization of Kelvin–Voigt viscoelastic fluid flow model

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Pages 2284-2307 | Received 11 Jul 2017, Accepted 30 Mar 2018, Published online: 15 Apr 2018

References

  • Pavlovskii VA . To the equation of theoretical description of weak aqueous polymer solutions. Sov Phys Dokl. 1971;200:809–812.
  • Oskolkov AP . The uniqueness and global solvability for boundary value problems for the equations of motion of water solutions of polymers. Zapiski Nauch Sem POMI. 1973;38:98–136.
  • Burtscher M , Szczyrba I . Numerical modeling of brain dynamics in traumatic situations -- impulsive translations. In: Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences; Las Vegas, Nevada, USA; 2005. p. 205–211.
  • Burtscher M , Szczyrba I . Computational simulation and visualization of traumatic brain injuries. In: Conference on Modeling, Simulation and Visualization Methods; Las Vegas, Nevada, USA; 2006. p. 101–107.
  • Cotter CS , Smolarkiewicz PK , Szezyrba IN . A viscoelastic model from brain injuries. Int J Numer Meth Fluids. 2002;40:303–311.
  • Cao Y , Lunasin EM , Titi ES . Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models Commun Math Sci. 2006;4:823–848.
  • Oskolkov AP . Theory of nonstationary flows of Kelvin-Voigt fluids. J Math Sci. 1985;28:751–758.
  • Oskolkov AP . Initial-boundary value problems for equations of motion of Kelvin--Voigt fluids and Oldroyd fluids. Proc Steklov Inst Math. 1989;2:137–182.
  • Oskolkov AP , Shadiev RD . Non local problems in the theory of the motion equations of Kelvin--Voigt fluids. J Math Sci. 1992;59:1206–1214.
  • Oskolkov AP , Shadiev RD . Towards a theory of global solvability on [0, ∞] of initial-boundary value problems for the equations of motion of Oldroyd and Kelvin-Voigt fluids. J Math Sci. 1994;68:240–253.
  • Bajpai S , Nataraj N , Pani AK , et al . Semidiscrete Galerkin method for equations of motion arising in Kelvin--Voigt model of viscoelastic fluid flow. Numer Methods PDEs. 2013;29:857–883.
  • Pany AK , Bajpai S , Pani AK . Optimal error estimates for semidiscrete Galerkin approximations to equations of motion described by Kelvin--Voigt viscoelastic fluid flow model. J Comput Appl Math. 2016;302:234–257.
  • Kalantarov VK , Titi ES . Global attractors and determining modes for the 3D Navier--Stokes--Voight equations. Chinese Ann Math Ser B. 2009;30:697–714.
  • Kalantarov VK . Global behavior of solutions of nonlinear equations of mathematical physics of classical and non-classical type [postdoctoral thesis]. St. Petersburg; 1988.
  • Kalantarov VK , Levant B , Titi ES . Gevrey regularity of the global attractor of the 3D Navier--Stokes--Voight equations. J Nonlinear Sci. 2009;19:133–152.
  • Sobolevskii PE . Stabilization of viscoelastic fluid motion (Oldroyd’s mathematical model). Differ Integral Equ. 1994;7:1597–1612.
  • He Y , Lin Y , Shen S , et al . On the convergence of viscoelastic fluid flows to a steady state. Adv Differ Equ. 2002;7:717–742.
  • He Y , Li Y . Asymptotic behavior of linearized viscoelastic flow problem. Discrete Contin Dyn Syst -Ser B. 2008;10:843–856.
  • Kesavan S . Topics in functional analysis and application. New Delhi: New Age International (P)Ltd Publishers; 2008.
  • Girault V , Raviart PA . Finite element approximation of the Navier--Stokes equations. Lecture notes in mathematics. New York (NY): Springer; 1981.
  • Temam R . Navier--Stokes equations, theory and numerical analysis. Amsterdam: North-Holland; 2002.

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