Hong-Ge Chen

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math.AP2026

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 $R$ with boundary value $u (x) = \frac{x}{∣ x ∣}$ is the degree-one radial solution of the planar…

math.AP2026

On Sirakov's equal-frequency uniqueness conjecture

Hong-Ge Chen, Yong Liu, Juncheng Wei +1

Let $N \in {2, 3}$ , $0 < μ_{1} \leq μ_{2}$ , and $0 < β < μ_{1}$ . 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…

math.AP2026

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 $u : R^{2} \to R^{2}$ of the Ginzburg--Landau equation $- Δ u = u (1 - ∣ u ∣^{2})$ with $∣ u (x) ∣ \to 1$ as $∣ x ∣ \to \infty$ has fi…