43 citations · 201 across the 69 of their papers we have counts for
72 papers
Domain dependence of Sobolev-curl constants and structure of critical curl-curl solutions
Yong Liu, Jun Wang, Xuan Wang +1
This paper investigates intrinsic critical Sobolev-curl constants on bounded domains and the structure of finite-energy solutions to the critical curl-curl equation in R^3. First,…
On Brezis' open problem 2.2
Hong-Ge Chen, Yong Liu, Juncheng Wei +1
We prove that the global minimizer of the Ginzburg-Landau energy in the disk of radius with boundary value is the degree-one radial solution of the planar…
Nonradial stable solutions near the Joseph--Lundgren threshold
Shibing Chen, Yong Liu, Juncheng Wei +1
We study positive stable solutions of the supercritical Lane--Emden equation in the first Joseph--Lundgren interval. For a family of dimensions, we construct nonradial stable entir…
Nondegeneracy and Morse Index of Ginzburg--Landau Vortices
Manuel del Pino, Yong Liu, Monica Musso +2
We prove that the standard degree-two and degree-three vortex solutions of the Ginzburg-Landau equation are nondegenerate. Their Morse indices are also computed. The proof relies o…
On Sirakov's equal-frequency uniqueness conjecture
Hong-Ge Chen, Yong Liu, Juncheng Wei +1
Let , , and . We prove that the equal-frequency two-component cubic Schrödinger system \[ -Δu+u=μ_1u^3+βuv^2, \qquad -Δv+v=μ_2v^3+βu^2v \quad\te…
Finite Potential Energy for Entire Solutions of the Planar Ginzburg--Landau Equation
Hongge Chen, Juncheng Wei, Haicheng Yan +1
We prove that every smooth entire solution of the Ginzburg--Landau equation with as has fi…
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…
Refined boundary layer asymptotics for elliptic equations with multiplicative nonlocal effects
Chiun-Chang Lee, Sang-Hyuck Moon, Wen Yang
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity…
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…
A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions
Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar +2
We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, w…
Oriented graphs on curve complex I: hyperbolic and extremal length
Dong Tan, Wen Yang
We investigate oriented graphs based on the curve complex of a closed surface and induced by functions on the vertex set of . In particular, we introduce the Dehn…
Bi-geodesic mappings between hyperbolic surfaces with boundary
Wen Yang
It is proved that a bijection between two compact hyperbolic surfaces with boundary is an isometry if it and its inverse map each geodesic onto some geodesic.
On Brezis' First Open Problem: A Complete Solution
Liming Sun, Juncheng Wei, Wen Yang
In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a…
The stability for F-Yang-Mills functional on CP^n
Yang Wen
In this paper, we study the critical points of -Yang-Mills functional on , which are called -Yang-Mills connections, which is a generalization of Yang-Mills co…
Boundary spike-layer solutions of the singular Keller-Segel system: existence, profiles and stability
Jose A. Carrillo, Jingyu Li, Zhi-An Wang +1
This paper is concerned with the boundary-layer solutions of the singular Keller-Segel model proposed by Keller-Segel (1971) in a multi-dimensional domain, where the zero-flux boun…
Non degeneracy of blow-up solutions of non-quantized singular Liouville-type equations and the convexity of the mean field entropy of the Onsager vortex model with singular sources
Daniele Bartolucci, Wen Yang, Lei Zhang
We establish the non-degeneracy of bubbling solutions for singular mean field equations when the blow-up points are either regular or involve non-quantized singular sources. This e…
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…
Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized singular mean field equations
Daniele Bartolucci, Wen Yang, Lei Zhang
For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quant…
Lump type solutions: Backlund transformation and spectral properties
Yong Liu, Jun-cheng Wei, Wen Yang
There are various different ways to obtain traveling waves of lump type for the KP equation. We propose a general and simple approach to derive them via a Backlund transformation.…
Uniqueness of lump solutions of KP-I equation
Yong Liu, Jun-cheng Wei, Wen Yang
The KP-I equation has family of solutions which decay to zero at space infinity. One of these solutions is the classical lump solution. This is a traveling wave, and the KP-I equat…
Affine Toda system of and type: compactness and affine Weyl group
Leilei Cui, Zhaohu Nie, Wen Yang
The local mass is a fundamental quantized information that characterizes the blow-up solution to the Toda system and has a profound relationship with its underlying algebraic struc…