Stokes系统响应算子图上单点的包络法

The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator

Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The method employs only a single pair of a quite natural Neumann data prescribed on the outer boundary and the corresponding Dirichlet data on the same boundary of the solution of the governing equation over a finite time interval, that is a single point on the graph of the so-called {\it response operator}. It is shown that the methods enables us to extract the d…

The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance

The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a finite time interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.

不可压缩 Navier-Stokes PDE 的孤立子解法

Solitary solution method for incompressible Navier-Stokes PDE

提出一种利用空间收缩求解不可压缩 Euler 和 Navier-Stokes PDE 的孤立子方法，将动量平流非线性响应移入收缩项，通过闭合函数求解连续性方程并引入 n+1 维验证任意非结构化网格。

On the derivation of a Stokes-Brinkman problem from Stokes equations around a random array of moving spheres

We consider the Stokes system in $\mathbb R^3,$ deprived of $N$ spheres of radius $1/N,$ completed by constant boundary conditions on the spheres. This problem models the instantaneous response of a viscous fluid to an immersed cloud of moving solid spheres. We assume that the centers of the spheres and the boundary conditions are given randomly and we compute the asymptotic behavior of solutions when the parameter $N$ diverges. Under the assumption that the distribution of spheres/centers is chaotic, we prove convergence in mean to the solution of a Stokes-Brinkman problem.

接触线全局适定性：二维纳维-斯托克斯流

Global Well-Posedness of Contact Lines: 2D Navier-Stokes Flow

本文基于Guo-Tice的先验估计，研究了满足接触线动态定律的粘性流体模型的全局适定性，通过构造无压弱解和人工正则化处理毛细力项，建立了二维自由表面的适定性理论。

不可压缩Navier--Stokes方程双参数双曲松弛的声学滤波与压力恢复

Linear Corrector Estimates and Corrected Pressure Convergence for a Two-Parameter Hyperbolic Relaxation of the Incompressible Navier--Stokes Equations

针对不可压缩Navier--Stokes方程的双参数双曲松弛，通过引入声学-应力校正器并利用补偿变量和Ladyzhenskaya不等式，在特定参数条件下证明了滤波压力的强恢复及误差界。