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Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 6

On the weak solutions and determining modes of the g-Benard problem

Meryem KAYA
Muharrem ÖZLÜK
Pages
1453–1466
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Then, we investigate the long-term dynamics; specifically, we derive upper bounds for the number of determining modes for this system.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study the existence and uniqueness of weak solutions of the g-Benard problem.
📊
Key Findings & Data:In this paper we study the existence and uniqueness of weak solutions of the g-Benard problem.
💡
Conclusion & Impact:Then, we investigate the long-term dynamics; specifically, we derive upper bounds for the number of determining modes for this system.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:B\'{e}nard convection · existence and uniqueness of weak solutions · determining modes

Abstract

In this paper we study the existence and uniqueness of weak solutions of the g-Benard problem. Then, we investigate the long-term dynamics; specifically, we derive upper bounds for the number of determining modes for this system.

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Cite This Article

KAYA, M., ÖZLÜK, M. (2022). On the weak solutions and determining modes of the g-Benard problem. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 6, 1453–1466. https://ajindex.com/articles/529836

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References (17)

  1. Bae, H., Roh, J., Existence of Solutions of the g-Navier-Stokes Equations, Taiwanese J. Math., 8, No. 1, 85-102, 2004.
  2. Boland, J. and Layton, W., Error analysis for finite element methods for steady natural convection problems, Numer. Funct. Anal. Optim., 11:5-6, 449-483, 1990, DOI: 10.1080/01630569008816383. Galdi,G.P., Lectures in Mathematical Fluid Dynamics, Birkhauser-Verlag, 2000.
  3. Farhat, A., Jolly, M.S., and Titi, E.S., Continuous Data Assimilation for the 2D Benard Convection Through Velocity Measurements Alone, Physica D, 303, 59-66, 2015.
  4. Foias, C., Jolly, M.S., Kravchenko, R., and Titi, E.S., A unified approach to determining forms for the 2D Navier-Stokes equations -- the general interpolants case, Russ. Math. Surv., 69, No. 2, 359-381, 2014.
  5. Foias, C., Manley, O., Rosa, R. and Temam, R., Navier - Stokes Equations and Turbulence, Encyclopedia of Mathematics and Its Applications, vol. 83, Cambridge University Press, 2004.
  6. Foias, C., Manley, O., Temam, R., Attractors for the Benard problem: Existence and physical bounds on their fractal dimension, Nonlinear Anal. Theory, Methods & Applications, 11, 939-967, 1987.
  7. Foias, C., Prodi, G., Sur le comportement global des solutions non stationnaires des equations de Navier-Stokes en dimension two, Rend. Sem. Mat. Univ., Padova, 39, 1-34, 1967.
  8. Hale, J.K., Raugel, G., A damped hyperbolic equation on thin domains, Trans. Amer. Math. Soc., 329, 185-219, 1992.
  9. Hale, J.K., Raugel, G., Partial differential equations on thin domains, Differ. Eq. Math. Phys., Birmingham, AL, 1990,
  10. Academic Press, Boston, 63-97, 1992.
  11. Hale, J. K., Raugel, G., Reaction - Diffusion equation on thin domains, J. Math. Pures Appl., 71, 33-95, 1992.
  12. Hoang, L.T., Incompressible Fluids in Thin Domains with Navier Friction Boundary Conditions (I), J. Math. Fluid Mech., 12, No. 3, 435-472, 2010.
  13. Hoang, L.T., Incompressible Fluids in Thin Domains with Navier Friction Boundary Conditions (II), J. Math. Fluid Mech., 15, 361-395, 2013.
  14. Hu, C., Navier-Stokes equations in 3D thin domains with Navier friction boundary condition, J. Differ. Equ., 236, No. 1, 133-163, 2007.
  15. Hu, C., Global strong solutions of Navier-Stokes equations with interface boundary in three-dimensional thin domains, Nonlinear Anal. 74, No. 12, 3964-3997, 2011.
  16. Iftimie, D., The 3D Navier - Stokes equations seen as a perturbation of the 2D Navier - Stokes equations, Bull. Soc. Math., France, 127, 473-517, 1999.
  17. Iftimie, D. and Raugel, G., Some results on the Navier-Stokes equa