Singularity Formation for the General Poiseuille Flow of Nematic Liquid Crystals

Chen, Geng; Sofiani, Majed

doi:10.1007/s42967-022-00190-5

Cited by 1 publication

(3 citation statements)

References 16 publications

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“…It is known that the solution of system (1.2) and (1.3) generically form finite time cusp singularity [12,13]. The goal of this paper is to establish a global existence of Hölder continuous solutions for the Cauchy problem (1.2)-(1.5) beyond singularity formation as stated in Theorem 1 below.…”

Section: Introductionmentioning

confidence: 94%

“…Note that singularity formation is unavoidable in general [13]. Similar to [12], we introduce a new variable…”

Section: Main Idea Of This Workmentioning

confidence: 99%

“…In a recent paper [13], the singularity formation for the general system (1.2) and (1.3) was established. As mentioned above, we are concerning with the global existence of the Cauchy problem for the general system (1.2) and (1.3).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals: The general Case

Chen¹,

Liu²,

Sofiani³

2023

Preprint

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In this work, we study the Cauchy problem of Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of two partial differential equations: One is a quasi-linear wave equation for the director field representing the crystallization of the nematics, and the other is a parabolic PDE for the velocity field characterizing the liquidity of the material. We extend the work in [Chen, et. al. Arch. Ration. Mech. Anal. 236 (2020), 839-891] for a special case to the general physical setup. The Cauchy problem is shown to have global solutions beyond singularity formation. Among a number of progresses made in this paper, a particular contribution is a systematic treatment of a parabolic PDE with only Hölder continuous diffusion coefficient and rough (worse than Hölder) nonhomogeneous terms.

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Section: Introductionmentioning

confidence: 94%

“…Note that singularity formation is unavoidable in general [13]. Similar to [12], we introduce a new variable…”

Section: Main Idea Of This Workmentioning

confidence: 99%

See 1 more Smart Citation

The Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals: The general Case

Chen¹,

Liu²,

Sofiani³

2023

Preprint

View full text Add to dashboard Cite

show abstract

Singularity Formation for the General Poiseuille Flow of Nematic Liquid Crystals

Cited by 1 publication

References 16 publications

The Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals: The general Case

The Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals: The general Case

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