Changxing Miao

activity

20242026

most citedOn Onsager's type conjecture for the inviscid Boussinesq equations

6 citations · 6 across the 9 of their papers we have counts for

collaborators

12 papers

math.AP2026

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n \geq 3$

Han Cheng, Changxing Miao, Xiaohua Yao

We study endpoint mapping properties of low-energy wave operators for Schrödinger operators $H = - Δ + V$ on $R^{n}$ , $n \geq 3$ . In dimension four, we prove that a zero-energy reson…

math.CA2026

The Szemerédi-Trotter Estimate in Finite Field with its Applications

Changxing Miao, Rui Xie

We prove a sharp Szemerédi-Trotter estimate \[\mathcal{I}(A,\mathcal{L})\lesssim \frac{|A||\mathcal{L}|}{p}+|A|^{2/3}|\mathcal{L}|^{2/3}+|A|+|\mathcal{L}|\] for prime finite field…

math.AP2026

Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators

Han Cheng, Changxing Miao, Xiaohua Yao

We establish sharp endpoint mapping properties for the wave operators $W_{\pm} (H, - Δ)$ of two-dimensional Schrödinger operators $H = - Δ + V$ with real-valued decaying potentials $V$ . Toge…

math.NT2026

A multidimensional Szemerédi theorem in integers

Jingwei Guo, Changxing Miao, Guoqing Zhan

For any integer $n \geq 2$ , let $(m_{1}, \dots, m_{n})$ be a strictly increasing $n$ -tuple of positive integers. We show that any subset $A \subset [N]^{n}$ of density at least $(\log…

math.CA2025

Improvement of Pólya's conjecture for balls and cylinders

Jingwei Guo, Changxing Miao, Weiwei Wang +1

Pólya's conjecture on the eigenvalues of the Laplacian has been one of the core problems in spectral geometry. Building upon the recent breakthrough works on Pólya's conjecture for…

math.AP2025

On Onsager-type conjecture for the Elsässer energies of the ideal MHD equations

Changxing Miao, Yao Nie, Weikui Ye

In this paper, we investigate the ideal magnetohydrodynamics (MHD) equations on tours $\TTT^d$. For $d = 3$ , we resolve the flexible part of Onsager-type conjecture for Elsässer ener…

math.AP2024

Non-uniqueness of weak solutions to the Navier-Stokes equations in R^3

Changxing Miao, Yao Nie, Weikui Ye

To our knowledge, the convex integration method has been widely applied to the study of non-uniqueness of solutions to the Naiver-Stokes equations in the periodic region, but there…

math.AP2024

Sharp non-uniqueness for the Navier-Stokes equations in R^3

Changxing Miao, Yao Nie, Weikui Ye

In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the incompressible Navier-Stokes equations in $R^{3}$ . To be more precise, we exhibit the…

math.NT2024

$L^{p}$ maximal estimates for Weyl sums with $k \geq 3$ on $T$

Xuezhi Chen, Changxing Miao, Jiye Yuan +1

In this paper, we study the $L^{p}$ maximal estimates for the Weyl sums $\sum_{n = 1}^{N} e^{2 π i (n x + n^{k} t)}$ with higher-order $k \geq 3$ on $T$ , and obtain the positive and ne…

math.AP2024★ 6 cited

On Onsager's type conjecture for the inviscid Boussinesq equations

Changxing Miao, Yao Nie, Weikui Ye

In this paper, we investigate the Cauchy problem for the three dimensional inviscid Boussinesq system in the periodic setting. For $1 \leq p \leq \infty$ , we show that the threshold re…

math.AP2024

Bochner-Riesz means for critical magnetic Schrödinger operators in $R^{2}$

Changxing Miao, Lixin Yan, Junyong Zhang

We study $L^{p}$ -boundedness of the Bochner-Riesz means for critical magnetic Schrödinger operators $\LL_{\A}$ in $R^{2}$ , which involve the {physical} Aharonov-Bohm potentia…

math.CA2024

Two-point polynomial patterns in subsets of positive density in $R^{n}$

Xuezhi Chen, Changxing Miao

Let $γ (t) = (P_{1} (t), \dots, P_{n} (t))$ where $P_{i}$ is a real polynomial with zero constant term for each $1 \leq i \leq n$ . We will show the existence of the configuration ${x, x + γ (t)}$ …

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions n≥3

The Szemerédi-Trotter Estimate in Finite Field with its Applications

Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators

A multidimensional Szemerédi theorem in integers

Improvement of Pólya's conjecture for balls and cylinders

On Onsager-type conjecture for the Elsässer energies of the ideal MHD equations

Non-uniqueness of weak solutions to the Navier-Stokes equations in R^3

Sharp non-uniqueness for the Navier-Stokes equations in R^3

Lp maximal estimates for Weyl sums with k≥3 on T

On Onsager's type conjecture for the inviscid Boussinesq equations

Bochner-Riesz means for critical magnetic Schrödinger operators in R2

Two-point polynomial patterns in subsets of positive density in Rn

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n \geq 3$

$L^{p}$ maximal estimates for Weyl sums with $k \geq 3$ on $T$

Bochner-Riesz means for critical magnetic Schrödinger operators in $R^{2}$

Two-point polynomial patterns in subsets of positive density in $R^{n}$