Guolin Qin

activity

20182026

most citedLiouville type theorems for fractional and higher order Hénon-Hardy type equations via the method of scaling spheres

52 citations · 198 across the 31 of their papers we have counts for

collaborators

33 papers

math.AP2026

Lamb dipole stability without sign condition

Ken Abe, Kyudong Choi, In-Jee Jeong +1

For the 2D incompressible Euler equations on the half-plane, we establish Lyapunov stability of the Lamb dipole without sign condition on the vorticity. The main challenge arises f…

math.AP2026

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…

math.AP2026

Optimal Rigidity Results for the $k$ -Hessian Equation of Lane--Emden Type

Wei Dai, Jingze Fu, Changfeng Gui +1

In this paper, we establish optimal Liouville theorems and classification results for the $k$-Hessian Lane--Emden equation \[ σ_k(-D^2u)=u^p\quad\text{in }\R^n,\qquad -D^2u\in\ov…

math.AP2026

Smooth Failure of Boundary Unique Continuation for Harmonic Functions

Guolin Qin, Weicheng Zhan

For every $n \geq 3$ , we construct a nonconstant real-valued function $U \in C^{\infty} (R_{+}^{n})$ , harmonic in the upper half-space, whose complete boundary jet vanish…

math.AP2026

A Pohozaev-type neck proof of a conditional Harnack inequality in the critical $p$ -Laplacian setting

Guolin Qin, Yi Ru-Ya Zhang

We prove a conditional Schoen-type Harnack inequality for positive weak solutions of the critical $p$ -Laplace equation $- Δ_{p} u = g (u), 1 < p < n,$ under a global critical Sobol…

math.AP2026

Flexibility and rigidity for the Couette flow in the infinite channel

Dengjun Guo, Xiaoyutao Luo, Guolin Qin

We investigate the existence of stationary and traveling wave solutions to the 2D Euler equations near the Couette flow in the infinite channel $R \times [- 1, 1]$ . For Sobo…

math.AP2024

Helical kelvin waves for the 3D Euler equation

Daomin Cao, Boquan Fan, Rui Li +1

Helical Kelvin waves were conjectured to exist for the 3D Euler equations in Lucas and Dritschel \cite{LucDri} (as well as in \cite{Chu}) by studying dispersion relation for infini…

math.AP2023★ 2 cited

Method of scaling spheres: Liouville theorems in inner or outer (unbounded or bounded) generalized radially convex domains, blowing-up analysis on domains with not necessarily $C^{1}$ boundary and other applications

Wei Dai, Guolin Qin

In this paper, we aim to introduce the method of scaling spheres (MSS) as a unified approach to Liouville theorems on general domains in $R^{n}$ , and apply it to establish Li…

math.AP2023★ 1 cited

Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation

Daomin Cao, Shanfa Lai, Guolin Qin

In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds fo…

math.AP2022★ 2 cited

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…

math.AP2022

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…

math.AP2022

Traveling vortex pairs for 2D Boussinesq equations

Daomin Cao, Shanfa Lai, Guolin qin

In this paper, we study the existence and asymptotic properties of the traveling vortex pairs for the two-dimensional inviscid incompressible Boussinesq equations. We construct a f…

math.AP2022★ 2 cited

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…

math.AP2021

Co-rotating and traveling vortex sheets for the 2D incompressible Euler equation

Daomin Cao, Guolin Qin, Changjun Zou

We construct co-rotating and traveling vortex sheets for 2D incompressible Euler equation, which are supported on several small closed curves. These examples represent a new type o…

math.AP2021★ 1 cited

Existence of stationary vortex sheets for the 2D Euler equation

Daomin Cao, Guolin Qin, Changjun Zou

We investigate a steady planar flow of an ideal fluid in a (bounded or unbounded) domain $Ω \subset R^{2}$ . Let $κ_{i} \neq = 0$ , $i = 1, \dots, m$ , be $m$ arbitrary fixed constants…

math.AP2021

Classification of solutions to conformally invariant systems with mixed order and exponentially increasing or nonlocal nonlinearity

Wei Dai, Guolin Qin

In this paper, without any assumption on $v$ and under extremely mild assumption $u (x) = O (∣ x ∣^{K})$ at $\infty$ for some $K ≫ 1$ arbitrarily large, we prove classification of soluti…

math.AP2021