10 papers
Rigidity of a -curvature-type problem on in every dimension
Changfeng Gui, Yeyao Hu, Tuoxin Li +3
We prove that for every , every solution to the -curvature-type problem $$ αP_N u + (N-1)!\left(1-\frac{e^{Nu}}{\int_{\mathbb{S}^N} e^{Nu}dw}\right)=0 \ \ \ \ \ \mbox{o…
Planar Gross--Pitaevskii traveling waves at every subsonic speed
Changfeng Gui, Shanfa Lai, Guolin Qin +1
For every subsonic speed , we prove the existence of a finite-energy traveling wave for the planar Gross--Pitaevskii equation. This resolves the longstanding proble…
A positive answer to the generalized Chang-Yang conjecture on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every integer and , Beckner's inequality \[ \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\frac{(N-1)!}{N}\l…
Axially Symmetric Rigidity for a -Curvature-Type Equation on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every even integer or , every axially symmetric solution to the -curvature-type problem $$ αP_N u + (N-1)!(1-\frac{e^{Nu}}{\int_{\math…
Symmetry breaking for the complex sine-Gordon equation
Shibing Chen, Changfeng Gui, Yong Liu +2
We consider the existence of vortex solutions to the complex sine-Gordon II (CSG2) equation, which can be viewed as an analogy of the Ginzburg-Landau (GL) equation. Using the nontr…
On two-dimensional steady compactly supported Euler flows with constant vorticity
Changfeng Gui, Jun Wang, Wen Yang +1
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are pertu…
Stability of Solitary Capillary-Gravity Water Waves in Three Dimensions
Changfeng Gui, Shanfa Lai, Yong Liu +2
This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under stro…
Bifurcation analysis of Stokes waves with piecewise smooth vorticity in deep water
Changfeng Gui, Jun Wang, Wen Yang +1
In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water…
From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem
Changfeng Gui, Shanfa Lai, Yong Liu +2
In this paper, we study the three-dimensional gravity-capillary water wave problem involving an irrotational, perfect fluid with gravity and surface tension. We focus on steady wav…
Toda lattice and Riemann type minimal surfaces
Changfeng Gui, Yong Liu, Jun Wang +1
Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing config…