GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS COUPLED WITH THE HEAT EQUATION: EXISTENCE RESULT AND TIME DISCRETE APPROXIMATION

G. Deugoue; J. K. Djoko; A. C. Fouape

doi:10.11948/20200409

2021 Volume 11 Issue 5

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G. Deugoue, J. K. Djoko, A. C. Fouape. GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS COUPLED WITH THE HEAT EQUATION: EXISTENCE RESULT AND TIME DISCRETE APPROXIMATION[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2423-2458. doi: 10.11948/20200409

Citation:

G. Deugoue, J. K. Djoko, A. C. Fouape. GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS COUPLED WITH THE HEAT EQUATION: EXISTENCE RESULT AND TIME DISCRETE APPROXIMATION[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2423-2458. doi: 10.11948/20200409

GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS COUPLED WITH THE HEAT EQUATION: EXISTENCE RESULT AND TIME DISCRETE APPROXIMATION

1.
Universite de Dschang, Departement de Mathematiques et Informatique, Cameroun
2.
African peer review mechanism, Johannesburg, South Africa
3.
Universite de Dschang, Departement de Mathematiques et Informatique, Cameroun

Author Bio: Email: agdeugoue@yahoo.fr(G. Deugoue); Email: adeletsanou@yahoo.fr(A. C. Fouape)
Corresponding author: Email: jules.djokokamdem@gmail.com(J. K. Djoko)

Abstract

Abstract

We provide in this article an investigation of the globally modified Navier-Stokes problem coupled with the heat equation. After deriving the variational formulation of this problem, we prove the existence and the uniqueness of the solution using the method of Faedo-Galerkin and some compactness results. Next, we propose a time discretization of these equations based on Euler's implicit scheme. We prove the existence of solution with the aid of Brouwer's fixed point and study the stability of discrete in time solution by using the energy approach.
- Globally modified Navier Stokes /
- heat equation /
- Galerkin method /
- Brouwer fixed point /
- implicit Euler scheme
MSC: 65M12, 76D05

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References

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