Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity

2025/07/07 by Li, Jiaxu, Mei, Yu, Zhang, Rong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.04760

Abstract

This paper concerns the Cauchy problem of three-dimensional compressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficients μ₁(ρ),μ₂(ρ) are power functions of the density with the power larger than 1, it is proved that the system exists a unique global strong solution as long as the initial density is sufficiently large and L³-norm of the derivative of the initial director is sufficiently small. This is the first result concerning the global strong solution for three-dimensional compressible liquid crystal flows without smallness of velocity.

Citations

• Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity
• Global large strong solutions to the compressible Navier-Stokes equations with density-dependent viscosities, case I: isentropic flows
• Global Existence of Entropy-Weak Solutions to the Compressible Navier-Stokes Equations with Non-Linear Density Dependent Viscosities
• Well-posedness of three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum
• Global well-posedness of regular solutions to the three-dimensional isentropic compressible Navier-Stokes Equations with degenerate viscosities and vacuum
• Singularity formation for the two-dimensional harmonic map flow into S²
• Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
• On classical solutions for viscous polytropic fluids with degenerate viscosities and vacuum
• Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three
• Global existence of weak solutions of the nematic liquid crystal flow in dimensions three
• On classical solutions to 2D Shallow water equations with degenerate viscosities
• On Classical Solutions to the Cauchy Problem of the Two-Dimensional Barotropic Compressible Navier-Stokes Equations with Vacuum
• Global Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions
• Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces
• Global Well-Posedness of Classical Solutions to the Cauchy problem of Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data
• Global Well-Posedness of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes Equations
• Some constitutive equations for liquid crystals
• Harmonic Mappings of Riemannian Manifolds

Related

• Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity
• Global strong solution to the density-dependent incompressible flow of liquid crystals
• Global large solutions and incompressible limit for the compressible flow of liquid crystals
• Strong Solution to the Density-dependent Incompressible Nematic Liquid Crystal Flows
• Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals