Logarithmically improved BKM's criterion for the 3D nematic liquid crystal flows

DOI10.1016/j.na.2012.04.009zbMath1393.76010OpenAlexW1985004665MaRDI QIDQ435064

Qiao Liu, Shang-bin Cui, Ji-Hong Zhao

Publication date: 16 July 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.04.009

zbMATH Keywords

Euler equationsStokes equationsNavierEricksen-Leslie modelregularity Beale-Kato-Majda criterion

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Liquid crystals (76A15)

Related Items (3)

Local well-posedness and blow-up criteria of magneto-viscoelastic flows ⋮ Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows ⋮ An Osgood type regularity criterion for the liquid crystal flows

Cites Work

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• On energetic variational approaches in modeling the nematic liquid crystal flows
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Remarks on a paper by J. T. Beale, T. Kato, and A. Majda (Remarks on the breakdown of smooth solutions for the 3-dimensional Euler equations)
• Bilinear estimates in \(BMO\) and the Navier-Stokes equations
• An extension of the Beale-Kato-Majda criterion for the Euler equations
• A new regularity class for the Navier-Stokes equations in \(\mathbb{R}^ n\)
• Logarithmically improved criteria for Euler and Navier-Stokes equations
• On the regularity of weak solutions to the magnetohydrodynamic equations
• Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena
• Structure of the set of stationary solutions of the navier‐stokes equations
• Nonparabolic dissipative systems modeling the flow of liquid crystals

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