Existence of Solutions for the Ericksen-Leslie System

By F. Lin, Chun Liu. 2000

303 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e3c9489ecd087704b7f4ff3a6cf2ed0e46b23e63

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Zhen Lei
2. Marius Paicu
3. Arghir Zarnescu
4. Yi Zhou
5. Chun Liu
6. Min-Chun Hong
7. Jie Shen
8. Nader Masmoudi

In Geometry and Topology

1. Arghir Zarnescu
2. Marius Paicu
3. Yi Zhou
4. Chun Liu
5. Zhen Lei
6. Min-Chun Hong

Citations in the corpus

• A diffuse-interface method for simulating two-phase flows of complex fluids (2004, background): “Based on such energy laws, Lin & Liu (1995, 2000) have established the existence of classical and weak solutions for Leslie–Ericksen fluids.”
• Global Solutions for Incompressible Viscoelastic Fluids (2008, methodology): “The existence results we obtain in this paper, together with the methods, are valid in many related systems, such as those for general polymeric materials [5, 19], magnetohydrodynamics (MHD) [9], liquid crystals [10, 24 ], and the free interface motion in mixture problems [38].”
• Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, methodology): “The Ericksen-Leslie-Parodi system describing nematic liquid crystals, whose structure is closer to our system (but that has one less derivative in the forcing term of the Navier-Stokes equations) was studied in [12], [13], [19].”
• Global existence of solutions of the simplified Ericksen–Leslie system in dimension two (2011, background): “[3], [4]), which is probably the simplest mathematical system one can derive without destroying the basic nonlinear structure, for modelling the liquid crystal flow.”
• Regularity and Existence of Global Solutions to the Ericksen–Leslie System in $${\mathbb{R}^2}$$R2 (2013, unknown): “For example, Lin-Liu [22] and Wu-Xu-Liu [34] have considered its Ginzburg-Landau approximation: ∂tu+ u · ∇u+∇P = −∇ · (∇d ⊙∇d) +∇ · (σL(u, d)), ∇ · u = 0, ∂td+ u · ∇d− Ωd+ λ2λ1Ad = 1 |λ1| ( ∆d+ 1 ǫ2 (1− |d|2)d ) , (1.11) and have established the existence of global weak solutions, and the local e”