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

Xuanjiang Liu, Fuyi Xu and Peng Fu

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

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 |∇d|2d 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 |∇d|2d for small initial data. Lastly, we also get analyticity of the solution.

Date: 2022
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https://doi.org/10.1155/2022/3317007

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:3317007

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