Steady state and long time convergence of spirals moving by forced mean curvature motion

Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations

In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in $\Bbb R^N$. If we assume "single signedness condition" on the force, then we can show that a $C^1 (\Bbb R^N)$ solution $(v,p)$ with $|v|^2+ |p|\in L^{\frac{q}{2}}(\Bbb R^N)$, $q\in (\frac{3N}{N-1}, \infty)$ is trivial, $v=0$. For the solution of of the steady Navier-Stokes equations, satisfying $v(x)\to 0$ as $|x|\to \infty$, the condition $\int_{\Bbb R^3} |Δv|^{\frac65} dx<\infty$, which is stronger than the important D-condition, $\int_{\Bbb R^3} |\nabla v|^2 dx <\in…

有界区域中随机受迫 Euler–Poisson 方程的稳态解：第1部分。三维绝缘边界

Stationary solution to Stochastically Forced Euler-Poisson Equations in Bounded Domain: Part 1. 3-D Insulating Boundary

本文研究三维有界区域内带绝缘边界的随机 Euler–Poisson 方程，通过加权能量估计证明解的全局存在唯一性、指数收敛到稳态，并确定其不变测度为稳态 Dirac 测度。

有界域中随机强迫欧拉-泊松方程的稳态解：第二部分. 一维欧姆接触边界

Stationary solution to Stochastically Forced Euler-Poisson Equations in Bounded Domain: Part 2. 1-D Ohmic Contact Boundary

本文针对带欧姆接触边界的一维随机欧拉-泊松方程，利用Banach不动点定理和加权能量估计证明稳态附近解的全局存在性与渐近稳定性，并证明不变测度为稳态对应的Dirac测度。

随机强迫三维欧拉方程的耗散解

Dissipative solutions to randomly forced 3D Euler equations

本文提出了一种随机强迫三维欧拉方程的耗散解构造方法，并证明了其非唯一 ergodic 性

A variational approach to reaction diffusion equations with forced speed in dimension 1

We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or not, that is, we want to determine the large-time behaviour of the associated solution. This problem has been solved recently when the nonlinearity is of KPP type. We consider in the present paper general reaction terms, that are only assumed to be negative at infinity. Using a variational approach, we construct two thresholds determining the existence and th…

环形区域中具有非零角速度的径向对称螺旋流的亚声速时间周期解

Subsonic time-periodic solutions to radially symmetric spiral flows in an annulus

研究环形区域中具有非零角速度的径向对称非等熵欧拉系统的亚声速时间周期解，在特定边界条件下建立其存在性与稳定性，克服导数损失等困难，关键在于重写熵的径向导数及控制扰动积累。

源于不规则数据的 Navier-Stokes 方程稳态解的存在性与正则性

Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data

本文研究了 $\mathbb{R}^n_+$ 中强迫不可压缩定常 Navier-Stokes 流，证明了齐次 Sobolev 空间中小数据解的存在性与局部正则性，并基于非齐次 Stokes 系统推导出具有独立意义的可解性结果。

二维完美流体中的对数螺线

Logarithmic spirals in 2d perfect fluids

研究二维欧拉方程对数螺线解，证明局部与全局适定性，刻画长时间行为：解要么爆破要么完全均匀化，并实现涡片动力学为光滑解的极限。