arXiv subjects

Xiaoyu Xi

Publications and source records attributed to Xiaoyu Xi.

3 recordsLinked to original sources

arXiv2021

Existence and stability of stationary solutions to the compressible quantum model

In this paper, the compressible quantum model with the given mass source and the external force of general form in three-dimensional whole space is considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the existence and uniqueness of stationary solutions can be obtained by the contraction mapping principle. By using a general energy method, the nonlinear stability of stationary solutions is studied, and the time decay rates of the solutions are established when the initial perturbation belongs to $\dot{H}^{-s}$ with $0 \leq s < \frac{3}{2}$.

math.AP↗

arXiv2016

Uniform Regularity and Vanishing Viscosity Limit for the Nematic Liquid Crystal Flows in Three Dimensional Domain

In this paper, we investigate the uniform regularity and vanishing limit for the incompressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the incompressible nematic liquid crystal flows with boundary condition in a finite time interval which is independent of the viscosity. The solution is uniformly bounded in a conormal Sobolev space. Finally, we also study the convergence rate of the viscous solutions to the inviscid ones.

math.AP↗

arXiv2016

On a compressible non-isothermal model for nematic liquid crystals

We prove the existence of a weak solution to a non-isothermal compressible model for nematic liquid crystals. An initial-boundary value problem is studied in a bounded domain with large data. The existence of a global weak solution is established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ>3/2.

math.AP↗