## Harmonic Analysis and Differential Equations Student Seminar: Small data global regularity for simplified 3-D Ericksen-Leslie’s compressible hyperbolic liquid crystal model

Seminar | November 26 | 3:40-5 p.m. | 740 Evans Hall

Jiaxi Huang, USTC

Department of Mathematics

In this talk, we will consider the Ericksen-Leslie's hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity for small and smooth initial data near equilibrium is proved for the case that the system is a nonlinear coupling of compressible Navier-Stokes equations with wave map to $\mathbb { S }^2$. Our argument is a combination of vector field method and Fourier analysis. The main strategy to prove global regularity relies on an interplay between the control of high order energies and decay estimates, which is based on the idea inspired by the method of space-time resonances. In particular, the different behaviors of the decay properties of the density and velocity field for compressible fluids at different frequencies play a key role. Joint work with Ning Jiang, Yi-Long Luo, and Lifeng Zhao.

wangjian@berkeley.edu