Approximation of the trajectory attractor of the 3D smectic-A liquid crystal flow equations

Xiuqing Wang; Yuming Qin; Alain Miranville

doi:10.3934/cpaa.2020168

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2020, Volume 19, Issue 7: 3805-3827. Doi: 10.3934/cpaa.2020168

This issue Previous Article Retraction: The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities Next Article Algebraic structure of the $ L_2 $ analytic Fourier–Feynman transform associated with Gaussian paths on Wiener space

Approximation of the trajectory attractor of the 3D smectic-A liquid crystal flow equations

1.
College of Information Science and Technology, Donghua University, Shanghai 201620, China
2.
Department of Mathematics, Institute for Nonlinear Sciences, Donghua University, Shanghai 201620, China
3.
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7648, SP2MI, Boulevard Marie et Pierre Curie-Téléport 2, F–6962 Chasseneuil Futuroscope Cedex, France

^*Corresponding author
^*Corresponding author

Received: October 31, 2019

Revised: January 31, 2020

Published: April 2020

This paper was supported in part by the NNSF of China with contract numbers 11671075, 11801068, 11971110 and the Graduate Innovation Fund Project of Donghua University with contract number CUSF-DH-D-2020077

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Abstract

In this paper, we first establish the existence of trajectory attractors for the 3D smectic-A liquid crystal flow system and 3D smectic-A liquid crystal flow-$ \alpha $ model, and then prove that the latter trajectory attractor converges to the former one as the parameter $ \alpha\rightarrow 0^{+} $.

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Mathematics Subject Classification: Primary: 76N10, 76N15; Secondary: 35M13, 35Q35, 53C35.

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