Chilin Zhang

collaborators

4 papers

math.AP2026

Flexibility and rigidity of steady states of the two-dimensional Euler equations in an infinite channel

Yupei Huang, Chunjing Xie, Chilin Zhang

We study steady solutions to the two-dimensional incompressible Euler equations in an infinite channel, whose far-field limits are uniformly non-stagnant shear flows. In the smooth…

math.AP2026

Classification of global solutions to the singular equation $- Δ u = f (X) \cdot u^{- γ}$ in a Lipschitz epigraphical cone

Yahong Guo, Congming Li, Chilin Zhang

We construct and classify all global solutions to the singular equation $- Δ u = f (X) \cdot u^{- γ}$ supported in a general Lipschitz epigraphical cone, where $f (X)$ is a locally Dini…

math.AP2025

A positive homogeneous fractional harmonic function in a Lipschitz cone

Chilin Zhang

We construct a positive function $u$ supported and solving $(- Δ)^{s} u = 0$ in a Lipschitz cone. Such a function is unique up to a constant multiplication. Moreover, we show that it i…

math.AP2025

Boundary regularity theory of the singular Lane-Emden-Fowler equation in a Lipschitz domain

Yahong Guo, Congming Li, Chilin Zhang

We study the singular Lane-Emden-Fowler equation \begin{equation} -Δu=f(X)\cdot u^{-γ} \end{equation} in a bounded Lipschitz domain $Ω$ , with the Dirichlet boundary condition and a…

Flexibility and rigidity of steady states of the two-dimensional Euler equations in an infinite channel

Classification of global solutions to the singular equation −Δu=f(X)⋅u−γ in a Lipschitz epigraphical cone

A positive homogeneous fractional harmonic function in a Lipschitz cone

Boundary regularity theory of the singular Lane-Emden-Fowler equation in a Lipschitz domain

Classification of global solutions to the singular equation $- Δ u = f (X) \cdot u^{- γ}$ in a Lipschitz epigraphical cone