On optimal boundary control of Ericksen-Leslie system in dimension two

DOI10.1007/s00526-019-1676-zzbMath1429.35176arXiv1811.03512OpenAlexW3001499127MaRDI QIDQ2291578

Qiao Liu, Jianfeng Zhou, Changyou Wang, Xiaotao Zhang

Publication date: 31 January 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.03512

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Liquid crystals (76A15)

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Optimal distributed control of a Allen-Cahn/Cahn-Hilliard system with temperature ⋮ Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids ⋮ On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum ⋮ Optimal distributed control of two-dimensional Navier-Stokes-Cahn-Hilliard system with chemotaxis and singular potential ⋮ Regularity of weak solutions to a class of nonlinear problem with non-standard growth conditions ⋮ On mathematical analysis of complex fluids in active hydrodynamics

Cites Work

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• Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows
• Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in \(\mathbb R^2\)
• Optimal boundary control of a simplified Ericksen-Leslie system for nematic liquid crystal flows in \(2D\)
• Global existence of solutions of the simplified Ericksen-Leslie system in dimension two
• On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals
• Global regularity and uniqueness of weak solution for the 2-D liquid crystal flows
• Regularity and existence of global solutions to the Ericksen-Leslie system in \({\mathbb{R}^2}\)
• Hydrostatic theory of liquid crystals
• Reproductivity for a nematic liquid crystal model
• Liquid crystal flows in two dimensions
• Regularity and time-periodicity for a nematic liquid crystal model
• On the evolution of harmonic mappings of Riemannian surfaces
• Compact sets in the space \(L^ p(0,T;B)\)
• Partial regularity of the dynamic system modeling the flow of liquid crystals
• Existence of solutions for the Ericksen-Leslie system
• Evolution of harmonic maps with Dirichlet boundary conditions
• On the general Ericksen-Leslie system: Parodi's relation, well-posedness and stability
• Optimal control of a parabolic equation with dynamic boundary condition
• Well-posedness and long term behavior of a simplified Ericksen-Leslie non-autonomous system for nematic liquid crystal flows
• Well-posedness of the Ericksen-Leslie system
• Some constitutive equations for liquid crystals
• Finite time singularity of the nematic liquid crystal flow in dimension three
• Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions
• Optimal Control of an Allen--Cahn Equation with Singular Potentials and Dynamic Boundary Condition
• Long-Time Behavior for a Hydrodynamic Model on Nematic Liquid Crystal Flows with Asymptotic Stabilizing Boundary Condition and External Force
• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three
• 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
• Optimization with PDE Constraints
• Constrained Dirichlet Boundary Control in $L^2$ for a Class of Evolution Equations
• Sufficient conditions for regularity and uniqueness of a 3D nematic liquid crystal model
• Existence of optimal controls for viscous flow problems
• Necessary and sufficient conditions for optimal controls in viscous flow problems
• Boundary Value Problems and Optimal Boundary Control for the Navier--Stokes System: the Two-Dimensional Case
• Second order methods for boundary control of the instationary Navier-Stokes system
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Nonparabolic dissipative systems modeling the flow of liquid crystals
• Optimal Boundary Control for the Evolutionary Navier--Stokes System: The Three-Dimensional Case
• Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System

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