Zexi Wang

Uniqueness of prescribed-node radial bound states for a zero-mass double-power equation

Wenjing Chen, Zexi Wang

We study radial bound states of \[ Δu-\abs{u}^{q-1}u+\abs{u}^{p-1}u=0 \quad\text{in }\R^n, \qquad n\ge3,\qquad 1<q<p<\frac{n+2}{n-2}. \] For every integer $k \geq 1$ , we prove that th…

Flexibility for the Three-Dimensional Navier-Stokes Equations via Moving Hill Vortices

Quoc-Hung Nguyen, Zexi Wang

We construct weak solutions of the three-dimensional incompressible Navier--Stokes equations on the torus. The convex-integration scheme is based on the moving-dipole construction…

Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group

Wenjing Chen, Zexi Wang

We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group $H^{n}$ , \begin{equatio…

Remainder terms and sharp quantitative stability for a nonlocal Sobolev inequality on the Heisenberg group

Wenjing Chen, Zexi Wang

In this paper, we study the following nonlocal Sobolev inequality on the Heisenberg group \begin{equation}\label{eq:HLS} S_{HL}(Q,μ) \left(\int_{\mathbb{H}^{n}}\int_{\mathbb{H}^{n}…

math.AP2025

An extension of Cabré-Chanillo theorem to the $p$ -laplacian

Massimo Grossi, Luigi Montoro, Berardino Sciunzi +1

In this paper, we study the critical points of stable solutions for the following $p$ -laplacian equation \begin{equation*} \begin{cases} -div\big(|\nabla u|^{p-2}\nabla u\big)=f(u)…

Construction of solutions for the critical polyharmonic equation with competing potentials

Wenjing Chen, Zexi Wang

In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=Q(|y'|,y'')u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathb…

Blowing-up solutions for the Choquard type Brezis-Nirenberg problem in dimension three

Wenjing Chen, Zexi Wang

In this paper, we are interested in the existence of solutions for the following Choquard type Brezis-Nirenberg problem \begin{align*} \left\{ \begin{array}{ll} -Δu=\displaystyle\B…

New type of solutions for a critical Grushin-type problem with competing potentials

Wenjing Chen, Zexi Wang

In this paper, we consider a critical Grushin-type problem with double potentials. By applying the reduction argument and local Pohouzaev identities, we construct a new family of s…

New type of solutions for the critical polyharmonic equation

Wenjing Chen, Zexi Wang

In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathbb{R}^3\time…

New Regularity Criteria for Navier-Stokes and SQG Equations in Critical Spaces

Yiran Xu, Ly Kim Ha, Haina Li +1

In this paper, we investigate some priori estimates to provide the critical regularity criteria for incompressible Navier-Stokes equations on $R^{3}$ and super critical surf…

Blow-up solutions concentrated along minimal submanifolds for asymptotically critical Lane-Emden systems on Riemannian manifolds

Wenjing Chen, Zexi Wang

Let $(M, g)$ and $(K, κ)$ be two Riemannian manifolds of dimensions $N$ and $m$ , respectively. Let $ω \in C^{2} (M)$ , $ω > 0$ . The warped product $\mathcal{M}…

Multiple blowing-up solutions for asymptotically critical Lane-Emden systems on Riemannian manifolds

Wenjing Chen, Zexi Wang

Let $(M, g)$ be a smooth compact Riemannian manifold of dimension $N \geq 8$ . We are concerned with the following elliptic system \begin{align*} \left\{ \begin{array}{ll} -…

math.AP2023★ 1 cited

Normalized solutions for a fractional $N / s$ -Laplacian Choquard equation with exponential critical nonlinearities

Wenjing Chen, Zexi Wang

In this paper, we are concerned with the following fractional $N / s$ -Laplacian Choquard equation \begin{align*} \begin{cases} (-Δ)^s_{N/s}u=λ|u|^{\frac{N}{s}-2}u +(I_μ*F(u))f(u),\ \…

Normalized ground states for a fractional Choquard system in $R$

Wenjing Chen, Zexi Wang

In this paper, we study the following fractional Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} (-Δ)^{1/2}u=λ_1 u+(I_μ*F(u,v))F_u (u,v), \quad\mbox{in}\ \ \…

Normalized solutions for a fractional Choquard-type equation with exponential critical growth in $R$

Wenjing Chen, Qian Sun, Zexi Wang

In this paper, we study the following fractional Choquard-type equation with prescribed mass \begin{align*} \begin{cases} (-Δ)^{1/2}u=λu +(I_μ*F(u))f(u),\ \ \mbox{in}\ \mathbb{R},…

Normalized ground states for a biharmonic Choquard system in $R^{4}$

Wenjing Chen, Zexi Wang

In this paper, we study the existence of normalized ground state solutions for the following biharmonic Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} Δ^2u=…