Global Well-Posedness and Analyticity for the Three-Dimensional Incompressible Nematic Liquid Crystal Flows in Scaling Invariant Spaces

Xuanjiang Liu, Fuyi Xu, Peng Fu and Luigi C. Berselli

Advances in Mathematical Physics, 2022, vol. 2022, 1-9

Abstract: The Cauchy problem for the three-dimensional incompressible flows of liquid crystals in scaling invariant spaces is considered. In this work, we exhibit three results. First, we prove the global well-posedness of mild solution for the system without the supercritical nonlinearity ∇d2d when the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients. Our second result is a proof of the global existence of mild solution in the time dependent spaces for the system including the term ∇d2d for small initial data. Lastly, we also get analyticity of the solution.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:3317007

DOI: 10.1155/2022/3317007

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