6 papers
Uniformly Rotating Vortex Patches with Arbitrarily Many Genuine Holes
Zhilong Xue, Weicheng Zhan
For every prescribed integer , we construct uniformly rotating unit-vorticity vortex patches for the planar Euler equation such that is connected and $\…
Smooth Failure of Boundary Unique Continuation for Harmonic Functions
Guolin Qin, Weicheng Zhan
For every , we construct a nonconstant real-valued function , harmonic in the upper half-space, whose complete boundary jet vanish…
Towards Embodiment Scaling Laws in Robot Locomotion
Bo Ai, Liu Dai, Nico Bohlinger +7
Cross-embodiment generalization underpins the vision of building generalist embodied agents for any robot, yet its enabling factors remain poorly understood. We investigate embodim…
Remarks on radial symmetry of stationary and uniformly-rotating solutions for the 2D Euler equation
Boquan Fan, Yuchen Wang, Weicheng Zhan
We prove that any uniformly rotating solution of the 2D incompressible Euler equation with compactly supported vorticity must be radially symmetric whenever its angular veloci…
Symmetry in Serrin-type overdetermined problems
Daomin Cao, Juncheng Wei, Weicheng Zhan
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overd…
Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc
Boquan Fan, Yuchen Wang, Weicheng Zhan
We study the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler equation in the unit disc, both in the smooth setting and the patch setting.…