Author

Wei-Cheng Zhan

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Preprint Sep 2026

Rigidity of stationary and uniformly rotating planar Euler flows in the $C^1$ Yudovich class

We prove a rigidity theorem for stationary and uniformly rotating solutions of the two-dimensional incompressible Euler equation with vorticity $ \omega_0\in C^1(\mathbb{R}^2)\cap L^1(\mathbb{R}^2) \cap L^\infty(\mathbb{R}^2). $ If the angular velocity $\Omega$ satisfies \[ \Omega\leq\frac12\inf_{\mathbb{R}^2}\omega_0...

Bo-Quan Fan, Yu-Chen Wang, Chun-Jing Xie et al. · 0 citations

Preprint Aug 2026

Smooth Failure of Boundary Unique Continuation for Harmonic Functions

For every $n\geq 3$, we construct a nonconstant real-valued function $U\in C^\infty(\overline{\mathbb R^n_+})$, harmonic in the upper half-space, whose complete boundary jet vanishes on a compact nowhere dense subset of $\partial\mathbb R^n_+$ of positive $(n-1)$-dimensional measure. The essential construction takes pl...

Guo-Lin Qin, Wei-Cheng Zhan · 0 citations