Liouville theorem for steady-state solutions of simplified Ericksen-Leslie system

2019/06/14 by Yihang Hao, Hao, Yihang, Xiangao Liu +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1906.06318

openalex publication_date 2019/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the steady simplified Ericksen-Leslie system. For three dimension, we obtain Liouville theorems if u and ∇ d satisfy the Galdi's[1] condition, or some decay conditions. Note that the simplified Ericksen-Leslie system becomes Navier-Stokes equations when d is constant vector.

Citations

• Some constitutive equations for liquid crystals

Related

• Global smooth solution to the simplified Ericksen-Leslie system in dimension three
• A Liouville Type Theorem for Steady-State Navier-Stokes Equations
• On rigidity of the steady Ericksen-Leslie system
• Sufficient conditions on Liouville type theorems for the 3D steady Navier-Stokes equations
• Liouville-type theorems for steady solutions to the Navier-Stokes system in a slab