Approximation of the long-time dynamics of the dynamical system generated by the Ericksen-Leslie equations

被引：0

作者：

Medjo, T. Tachim ^{[1
]}

Tone, C. ^{[2
]}

Tone, F. ^{[3
]}

机构：

[1] Florida Int Univ, Dept Math, DM413B Univ Pk, Miami, FL 33199 USA

[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[3] Univ West Florida, Dept Math & Stat, Pensacola, FL 32514 USA

来源：

ASYMPTOTIC ANALYSIS | 2025年 / 144卷 / 01期

关键词：

Ericksen-Leslie equations; implicit Euler scheme; long-time stability; attractors; NEMATIC LIQUID-CRYSTALS; STATIONARY STATISTICAL PROPERTIES; WEAK SOLUTION; WELL-POSEDNESS; CONSTITUTIVE EQUATIONS; GLOBAL EXISTENCE; ATTRACTORS; FLOW; UNIQUENESS; BEHAVIOR;

D O I：

10.3233/ASY-241941

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the long-time dynamics of the dynamical system generated by the Ericksen-Leslie model. More precisely, we discretize the Ericksen-Leslie equations in time using the implicit Euler scheme, and with the aid of the discrete Gronwall lemmas we prove that the scheme is uniformly bounded. Moreover, using the theory of the multi-valued attractors we prove in a particular case the convergence of the global attractors generated by the numerical scheme to the global attractor of the continuous system as the time-step approaches zero.

引用

页码：1081 / 1104

页数：24

共 51 条

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