From the Landau-de Gennes theory to the Ericksen-Leslie theory in dimension two

Xin, Zhouping; Zhang, Xiaotao

doi:10.48550/arxiv.2105.10652

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…It seems that their method only works for smooth initial values. Recently, Xin-Zhang [34] proved that the weak convergence also holds in…”

Section: Then We Havementioning

confidence: 99%

Existence and convergence of the Beris-Edwards system with general Landau-de Gennes energy

Feng¹,

Hong²,

Yu³

2021

Preprint

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In this paper, we investigate the Beris-Edwards system for both biaxial and uniaxial Q-tensors with a general Landau-de Gennes energy density depending on four non-zero elastic constants. We prove existence of the strong solution of the Beris-Edwards system for uniaxial Q-tensors up to a maximal time. Furthermore, we prove that the strong solutions of the Beris-Edwards system for biaxial Q-tensors converge smoothly to the solution of the Beris-Edwards system for uniaxial Q-tensors up to its maximal existence time. 2(1.3) with three positive material constants a, b, c.

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“…It seems that their method only works for smooth initial values. Recently, Xin-Zhang [34] proved that the weak convergence also holds in…”

Section: Then We Havementioning

confidence: 99%

Existence and convergence of the Beris-Edwards system with general Landau-de Gennes energy

Feng¹,

Hong²,

Yu³

2021

Preprint

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“…The resulting hydrodynamics are molecular models (such as Doi-Onsager [7]), tensor models (such as Beris-Edwards [4] and Qian-Sheng [27]) and vector models (such as Ericksen-Leslie [8,9,16]), respectively. The connections between theories at these three levels are studied extensively, both in the sense of formal expansion [15,10,13] and rigorous limit [38,21,39,20,24,40].…”

Section: Introductionmentioning

confidence: 99%

Rigorous biaxial limit of a molecular-theory-based two-tensor hydrodynamics

Li¹,

Xu²

2022

Preprint

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We consider a two-tensor hydrodynamics derived from the molecular model, where high-order tensors are determined by closure approximation through the maximum entropy state or the quasi-entropy. We prove the existence and uniqueness of local in time smooth solutions to the two-tensor system. Then, we rigorously justify the connection between the molecular-theorybased two-tensor hydrodynamics and the biaxial frame hydrodynamics. More specifically, in the framework of Hilbert expansion, we show the convergence of the solution to the two-tensor hydrodynamics to the solution to the frame hydrodynamics.

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From the Landau-de Gennes theory to the Ericksen-Leslie theory in dimension two

Cited by 2 publications

References 33 publications

Existence and convergence of the Beris-Edwards system with general Landau-de Gennes energy

Existence and convergence of the Beris-Edwards system with general Landau-de Gennes energy

Rigorous biaxial limit of a molecular-theory-based two-tensor hydrodynamics

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