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8 papers · 2 filters
Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics
Zhen Lei, Thomas C. Sideris, Yi Zhou
We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval , for initial data of th…
A priori bounds for a class of semi-linear degenerate elliptic equations
Genggeng Huang
In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\label{000} a^{ij}(x)\partial_{ij}u+b^i(x)\partial_i u +f(x,u)=0,\text{in}…
Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow
Maurizio Grasselli, Hao Wu
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the avera…
Global strong solution to a nonlinear Dirac type equation in one dimension
Yongqian Zhang
This paper studies a class of nonlinear massless Dirac equations in one dimension, which include the equations for massless Thirring model and massless Gross-Neveu model. Under the…
Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws
Gui-Qiang Chen, Wei Xiang, Yongqian Zhang
We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalue…
Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions
Zhen Lei, Dong Li, Xiaoyi Zhang
We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of harmonic maps equation. Under a natural geometric angle condition…