Existence of solutions to incompressible biaxial nematic liquid crystals flows. Issue 16 (2nd November 2022)

• Record Type: Journal Article
• Authors: Gong, Weihua; Lin, Junyu
• Is Part Of: Applicable analysis. Volume 101:Issue 16(2022)
• Page Start: 5872
• Page End: 5905
• Publication Date: 2022-11-02
• Subjects: Liquid crystal -- biaxial nematic -- incompressible flow -- global solution; 35A01 -- 35A09 -- 35Q35 -- 76D03; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1909723
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The recent paper considers the incompressible hydrodynamic flow of biaxial nematic liquid crystal in dimensions N with N = 2 or 3. The unique local solutions are firstly derived for ρ 0 ≥ 0 in dimensions 2 and 3. Then the unique global solution is obtained for 0 < M 1 ≤ ρ 0 and small initial energy: ∫ Ω ( ρ 0 | v 0 | 2 + | ∇ n 0 | 2 + | ∇ m 0 | 2 ) d x .