6 papers · 1 filter
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…
Classification of global solutions to the singular equation in a Lipschitz epigraphical cone
Yahong Guo, Congming Li, Chilin Zhang
We construct and classify all global solutions to the singular equation supported in a general Lipschitz epigraphical cone, where is a locally Dini…
A positive homogeneous fractional harmonic function in a Lipschitz cone
Chilin Zhang
We construct a positive function supported and solving in a Lipschitz cone. Such a function is unique up to a constant multiplication. Moreover, we show that it i…
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 , with the Dirichlet boundary condition and a…
Optimal H{ö}lder convergence of a class of singular steady states to the Bahouri-Chemin patch
Yupei Huang, Chilin Zhang
Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In \cite{elgindi2022regular}, a family of singular steady sta…
The boundary Harnack principle in a slit domain and its application to the Signorini problem
Chilin Zhang
We prove the regularity of the free boundary in the Signorini problem with variable coefficients. We use a boundary Harnack inequality in slit domain. The key m…