Regularity of the solutions to the liquid crystal equations with small rough data

Du, Yi; Wang, Keyan

doi:10.1016/j.jde.2013.07.066

Cited by 13 publications

(15 citation statements)

References 24 publications

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“…Subsequently, a lot of studies have been done on the existence and uniqueness of solutions for the incompressible nematic liquid crystal flow, cf. previous studies and the references therein.…”

Section: Introductionmentioning

confidence: 76%

Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

Yang

Tao

2017

Math Methods in App Sciences

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In this paper, we consider the time-periodic solution to a simplified version of Ericksen-Leslie equations modeling the compressible hydrodynamic flow of nematic liquid crystals with a time-periodic external force in a periodic domain in R N . By using an approach of parabolic regularization and combining with the topology degree theory, we establish the existence of the time-periodic solution to the model under some smallness and symmetry assumptions on the external force. Then, we give the uniqueness of the periodic solution of this model.

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Section: Introductionmentioning

confidence: 76%

Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

Yang

Tao

2017

Math Methods in App Sciences

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“…Recently, Wang in [38] used the framework of Koch and Tataru [20] to proved that if the initial data (u 0 , d 0 ) ∈ BM O −1 × BM O with small norm, then system (1.1)-(1.4) exists a global-in time Koch-Tataru type solution. For the regularity issues of solutions to system (1.1)-(1.4), in [7,8], Du and…”

Section: )mentioning

confidence: 99%

“…These useful properties It is easy to varify that the spaces L n (R n ) ×Ẇ 1,n (R n ) and and the existence space of Koch-Tataru type solutions to the nematic liquid crystal flows, for more details about these space, we refer to [7,8,20,22,38,41] and the references therein.…”

Section: )mentioning

confidence: 99%

Space–time derivative estimates of the Koch–Tataru solutions to the nematic liquid crystal system in Besov spaces

Liu

2015

Journal of Differential Equations

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In recent paper [7], Y. Du and K. Wang (2013) proved that the global-in-time Koch-Tataru type solution (u, d) to the n-dimensional incompressible nematic liquid crystal flow with small initial data (u 0 , d 0 ) in BMO −1 × BMO has arbitrary space-time derivative estimates in the so-called Koch-Tataru space norms. The purpose of this paper is to show that the Koch-Tataru type solution satisfies the decay estimates for any space-time derivative involving some borderline Besov space norms. More precisely, for the global-in-time Koch-Tataru type solution (u, d) to the nematic liquid crystal flow with initial data (u 0 , d 0 ) ∈ BMO −1 × BMO and u 0 BMO −1 + [d 0 ] BMO ≤ ε for some small enough ε > 0, and for any positive integers k and m, one hasFurthermore, we shall give that the solution admits a unique trajectory which is Hölder continuous with respect to space variables.

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“…Some progress has been made in the analysis of the simplified Ericksen‐Leslie system for an incompressible fluid; we can refer to Hong, Lin et al, and Lin and Wang() in the direction of weak solutions and for strong solutions as well as Hao and Liu and Huang and Wang() in the direction of the blow‐up criterion. See also Du and Wang, Li, and Wang() for some related discussions. We note that the compressible flow of liquid crystals is much more complex and difficult to explore by mathematical analysis.…”

Section: Introductionmentioning

confidence: 99%

On weak solution to the steady compressible flow of nematic liquid crystals

Tan

2019

Math Methods in App Sciences

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Regularity of the solutions to the liquid crystal equations with small rough data

Cited by 13 publications

References 24 publications

Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

Space–time derivative estimates of the Koch–Tataru solutions to the nematic liquid crystal system in Besov spaces

On weak solution to the steady compressible flow of nematic liquid crystals

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