Global Well-Posedness and Analyticity for the Three-Dimensional Incompressible Nematic Liquid Crystal Flows in Scaling Invariant Spaces. (2nd June 2022)

• Record Type: Journal Article
• Authors: Liu, Xuanjiang; Xu, Fuyi; Fu, Peng
• Other Names: Berselli Luigi C. Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2022(2022)
• Publication Date: 2022-06-02
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2022/3317007
• Languages: English
• ISSNs: 1687-9120

Abstract

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