Suitable Weak Solutions for the Co-rotational Beris–Edwards System in Dimension Three

In this paper, we establish the global existence of a suitable weak solution to the co-rotational Beris–Edwards Q -tensor system modeling the hydrodynamic motion of nematic liquid crystals with either Landau–De Gennes bulk potential in R 3 or Ball–Majumdar bulk potential in T 3 , a system coupling t...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2020-11, Vol.238 (2), p.749-803
Main Authors: Du, Hengrong, Hu, Xianpeng, Wang, Changyou
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Computational fluid dynamics
Fluid- and Aerodynamics
Liquid crystals
Mathematical and Computational Physics
Nematic crystals
Physics
Physics and Astronomy
Tensors
Theoretical
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Summary:In this paper, we establish the global existence of a suitable weak solution to the co-rotational Beris–Edwards Q -tensor system modeling the hydrodynamic motion of nematic liquid crystals with either Landau–De Gennes bulk potential in R 3 or Ball–Majumdar bulk potential in T 3 , a system coupling the forced incompressible Navier–Stokes equation with a dissipative, parabolic system of Q -tensor Q in R 3 , which is shown to be smooth away from a closed set Σ whose 1-dimensional parabolic Hausdorff measure is zero.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-020-01554-y