全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

The Asymptotic Behavior of Solutions for 3D Globally Modified Bénard Problem with Delay

DOI: 10.4236/oalib.1105163, PP. 1-15

Subject Areas: Partial Differential Equation, Fluid Mechanics

Keywords: Bénard System, Delay, Galerkin Approximation, Asymptotic Behavior

Full-Text   Cite this paper   Add to My Lib

Abstract

In this paper, we mainly study the existence and uniqueness of solutions and the asymptotic behavior of solutions for three-dimensional globally modified Bénard systems with delays under local Lipschitz conditions.

Cite this paper

Hou, X. and Zhu, C. (2019). The Asymptotic Behavior of Solutions for 3D Globally Modified Bénard Problem with Delay. Open Access Library Journal, 6, e5163. doi: http://dx.doi.org/10.4236/oalib.1105163.

References

[1]  Temam, R. (1988) Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4684-0313-8
[2]  Birnir, B. and Svanstedt, N. (2004) Existence Theory and Strong Attractors for the Rayleigh-Bénard Problem with a Large Aspect Ratio. Discrete & Continuous Dynamical Systems, 10, 53-74.
[3]  Caraballo, T., Márquez-Durán, A.M. and Real, J. (2010) Three-Dimensional System of Globally Modified Na-vier-Stokes Equations with Delay. International Journal of Bifurcation and Chaos in Applied Sciences, 20, 2869-2883.
https://doi.org/10.1142/S0218127410027428
[4]  Marn-Rubio, P., Márquez-Durán, A.M. and Real, J. (2013) Asymptotic Behavior of Solutions for a Three Dimensional System of Globally Modified Navier-Stokes Equations with a Locally Lipschitz Delay Term. Nonlinear Analysis, 79, 68-79.
https://doi.org/10.1016/j.na.2012.11.006
[5]  Romito, M. (2009) The Uniqueness of Weak Solutions of the Globally Modified Navier-Stokes Equations. Advanced Nonlinear Studies, 9, 425-429.
https://doi.org/10.1515/ans-2009-0209
[6]  Robinson, J.C. (2001) Infinite-Dimensional Dynamical Systems. Cambridge University Press, Cambridge. https://doi.org/10.1007/978-94-010-0732-0
[7]  Kapustyan, O.V., Melnik, V.S. and Valero, J. (2007) A Weak Attractor and Properties of Solutions for the Three-Dimensional Bénard Problem. Discrete & Continuous Dynamical Systems, 18, 449-481. https://doi.org/10.3934/dcds.2007.18.449
[8]  Temam, R. (1979) Na-vier-Stokes Equations. North-Holland, Amsterdam.
[9]  Lions, J.L. (1969) Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris.
[10]  Evans, L.C. (2010) Partial Differential Equations. American Mathematical Society, 22, 261-271. https://doi.org/10.1090/gsm/019

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413