Global well-posedness for the two-dimensional equations of nonhomogeneous incompressible liquid crystal flows with nonnegative density

DOI10.3934/dcdsb.2016065zbMath1354.35107arXiv1211.7140OpenAlexW1695948083MaRDI QIDQ325781

Jian-Wen Zhang, Sheng-quan Liu

Publication date: 11 October 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.7140

zbMATH Keywords

vacuumliquid crystalsblowup criterionglobal strong solutionsnonhomogeneous incompressible flows

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) A priori estimates in context of PDEs (35B45) Liquid crystals (76A15) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Blow-up in context of PDEs (35B44) Strong solutions to PDEs (35D35)

Related Items (7)

Global well-posedness for the density-dependent incompressible flow of liquid crystals ⋮ On global well-posedness and decay of 3D Ericksen-Leslie system ⋮ On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum ⋮ Global regularity to the 2D non-isothermal inhomogeneous nematic liquid crystal flows ⋮ Global existence and exponential decay of strong solutions to the 2D density-dependent nematic liquid crystal flows with vacuum ⋮ Global regularity to the 2D inhomogeneous liquid crystal flows with large initial data and vacuum ⋮ Strong solutions to Cauchy problem of 2D compressible nematic liquid crystal flows

Cites Work

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• Global existence of weak solution for the 2-D Ericksen-Leslie system
• Solutions of incompressible hydrodynamic flow of liquid crystals
• Global existence of solutions of the simplified Ericksen-Leslie system in dimension two
• Global solution to the incompressible flow of liquid crystals
• Global regularity and uniqueness of weak solution for the 2-D liquid crystal flows
• Global strong solution to the 2D nonhomogeneous incompressible MHD system
• Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data
• Hydrostatic theory of liquid crystals
• Compressible fluid flow and systems of conservation laws in several space variables
• Liquid crystal flows in two dimensions
• On the evolution of harmonic mappings of Riemannian surfaces
• Existence and partial regularity results for the heat flow for harmonic maps
• Blow-up and global existence for heat flows of harmonic maps
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• Heat flow and boundary value problem for harmonic maps
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• On coercive estimates for solutions of linear systems of hydrodynamic type
• On critical cases of Sobolev's inequalities
• Well-posedness of the Ericksen-Leslie system
• Some constitutive equations for liquid crystals
• Blow up Criterion for Nematic Liquid Crystal Flows
• Regularity of solutions to the liquid crystals systems in {\mathbb{R}}^2 and \mathbb{R}^3
• Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions
• Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena
• Global weak solution to the flow of liquid crystals system
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Strong Solutions of the Navier–Stokes Equations for Nonhomogeneous Incompressible Fluids
• Nonparabolic dissipative systems modeling the flow of liquid crystals

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