11 citations · 59 across the 30 of their papers we have counts for
32 papers
Rigidity of stationary and uniformly rotating planar Euler flows in the Yudovich class
Boquan Fan, Yuchen Wang, Chunjing Xie +1
We prove a rigidity theorem for stationary and uniformly rotating solutions of the two-dimensional incompressible Euler equation with vorticity $ ω_0\in C^1(\mathbb{R}^2)\cap L^1(\…
A Variational Family of Traveling Vortex Dipoles: Transition, Uniqueness, and Stability
Ken Abe, In-Jee Jeong, Guolin Qin +1
We provide a unified description of a stable variational family of traveling vortex dipoles for the two-dimensional incompressible Euler equations, connecting the classical Lamb di…
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…
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 velocit…
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…
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…
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.…
Free boundary problems for the two-dimensional Euler equations in exterior domains
Daomin Cao, Boquan Fan, Weicheng Zhan
In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain,…
On the rigidity of the 2D incompressible Euler equations
Yuchen Wang, Weicheng Zhan
We consider rigidity properties of steady Euler flows in two-dimensional bounded domains. We prove that steady Euler flows in a disk with exactly one interior stagnation point and…
A rigidity result for the Euler equations in an annulus
Yuchen Wang, Weicheng Zhan
We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and…
A Liouville theorem for the Euler equations in a disk
Yuchen Wang, Weicheng Zhan
We present a symmetry result regarding stationary solutions of the 2D Euler equations in a disk. We prove that in a disk, a steady flow with only one stagnation point and tangentia…
Uniqueness and stability of steady vortex rings for 3D incompressible Euler equation
Daomin Cao, Shanfa Lai, Guolin Qin +2
In this paper, we are concerned with the uniqueness and nonlinear stability of vortex rings for the 3D Euler equation. By utilizing Arnold 's variational principle for steady state…
Existence and Stability of the Lamb Dipoles for the Quasi-Geostrophic Shallow-Water Equations
Shanfa Lai, Guolin Qin, Weicheng Zhan
In this paper, we prove the nonlinear orbital stability of vortex dipoles for the quasi-geostrophic shallow-water (QGSW) equations. The vortex dipoles are explicit travelling wave…
Existence, uniqueness and stability of steady vortex rings of small cross-section
Daomin Cao, Guolin Qin, Weilin Yu +2
This paper is concerned with steady vortex rings in an ideal fluid of uniform density, which are special global axi-symmetric solutions of the three-dimensional incompressible Eule…
Kármán vortex street for the generalized surface quasi-geostrophic equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
We are concerned with the existence of periodic travelling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation(including incompressible Euler equation), kn…
On the global classical solutions for the generalized SQG equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new fami…
Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations
Daomin Cao, Guolin Qin, Weicheng Zhan +1
By applying implicit function theorem on contour dynamics, we prove the existence of co-rotating and travelling patch solutions for both Euler and the generalized surface quasi-geo…
Existence and stability of smooth traveling circular pairs for the generalized surface quasi-geostrophic equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
In this paper, we construct smooth travelling counter-rotating vortex pairs with circular supports for the generalized surface quasi-geostrophic equation. These vortex pairs are an…
Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and travelling global solutions for the gSQG e…
Global solutions for the generalized SQG equation and rearrangements
Daomin Cao, Guolin Qin, Weicheng Zhan +1
In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximiza…
Dynamic Underwater Acoustic Channel Tracking for Correlated Rapidly Time-varying Channels
Qihang Huang, Wei Li, Weicheng Zhan +2
In this work, we focus on the model-mismatch problem for model-based subspace channel tracking in the correlated underwater acoustic channel. A model based on the underwater acoust…
Traveling vortex pairs for 2D incompressible Euler equations
Daomin Cao, Shanfa Lai, Weicheng Zhan
In this paper, we study desingularization of vortices for the two-dimensional incompressible Euler equations in the full plane. We construct a family of steady vortex pairs for the…
On the steady axisymmetric vortex rings for 3-D incompressible Euler flows
Daomin Cao, Weicheng Zhan
In this paper, we study nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler flows. We construct a family of steady vortex rings (with and w…