9 papers · 1 filter
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…
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…
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…
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…
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.…