39 citations · 90 across the 6 of their papers we have counts for
6 papers
Global Well-posedness of Incompressible Elastodynamics in Three Dimensional Thin Domain
Yuan Cai, Fan Wang
In this article, we prove global existence of classical solutions to the incompressible isotropic Hookean elastodynamics in three-dimensional thin domain $Ω_δ=\mathbb{R}^2\times [0…
Uniform Bound of the Highest-order Energy of the 2D Incompressible Elastodynamics
Yuan Cai
This paper concerns the time growth of the highest-order energy of the systems of incompressible isotropic elastodynamics in two space dimensions. The global well-posedness of smoo…
Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium
Yuan Cai, Wei Wang
We study a simplified inertial Ericksen-Leslie system for the nematic liquid crystal flow, which can be viewed as a system coupling Navier-Stokes equations and wave map equations.…
Global Well-posedness for 2D Nonlinear Wave Equations without Compact Support
Yuan Cai, Zhen Lei, Nader Masmoudi
In the significant work of [2], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the…
Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions
Yuan Cai, Zhen Lei, Fanghua Lin +1
This paper studies the inviscid limit of the two-dimensional incompressible viscoelasticity, which is a system coupling a Navier-Stokes equation with a transport equation for the d…
Global Well-posedness of the Incompressible Magnetohydrodynamics
Yuan Cai, Zhen Lei
This paper studies the Cauchy problem of the incompressible magnetohydrodynamic systems with or without viscosity . Under the assumption that the initial velocity field and the…