Qianyun Miao

activity

20152026

most citedUniqueness of absolute minimizers for $L^\fz$-functionals involving Hamiltonians

H (x, p)

11 citations · 19 across the 14 of their papers we have counts for

collaborators

14 papers

math.AP2026

The $L^{p}$ Neumann problem for the Stokes system in nonsmooth domains

Qianyun Miao, Fa Peng

We study the $L^{p}$ Neumann problem for the Stokes system on bounded Lipschitz domains in $R^{n}$ with $n \geq 2$ . Our main contribution is to introduce a nonlinear gradient qua…

math.AP2026

Global regularity of temperature patches for the 3D non-diffusive Boussinesq system with large Prandtl number

Qianyun Miao, Jiakun Yang

So far the global well-posedness of strong solutions for the 3D non-diffusive Boussinesq system with large initial data remains a remarkable open problem. In this paper, we solve t…

math.AP2024

A nonlinear Calderón-Zygmund $L^{2}$ -theory for the Dirichlet problem involving $- ∣ D u ∣^{γ} Δ_{p}^{N} u = f$

Qianyun Miao, Fa Peng, Yuan Zhou

We establish a nonlinear Calderón-Zygmund $L^{2}$ -theory to the Dirichlet problem $$-|Du|^γΔ^N_p u=f\in L^2(Ω)\quad {\rm in}\quad Ω; \quad u=0 \ \mbox{on $\partialΩ$} $$ for $n \geq 2$ ,…

math.AP2024

Local regularity and finite-time singularity for a class of generalized SQG patches on the half-plane

Qianyun Miao, Changhui Tan, Liutang Xue +1

In this paper, we investigate a class of inviscid generalized surface quasi-geostrophic (SQG) equations on the half-plane with a rigid boundary. Compared to the Biot-Savart law in…

math.AP2023

Global well-posedness and refined regularity criterion for the uni-directional Euler-alignment system

Yatao Li, Qianyun Miao, Changhui Tan +1

We investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $ϕ (x) = ∣ x ∣^{- (d + α)}$ for $α…

math.AP2022

A global second order Sobolev regularity for $p$ -Laplacian type equations with variable coefficients in bounded domains

Qianyun Miao, Fa Peng, Yuan Zhou

Let $Ω \subset R^{n}$ be a bounded convex domain with $n \geq 2$ . Suppose that $A$ is uniformly elliptic and belongs to $W^{1, n}$ when $n \geq 3$ or $W^{1, q}$ for some $q > 2$ when $n = 2$ . Fo…

math.AP2022

Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment

Xiang Bai, Qianyun Miao, Changhui Tan +1

In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in…

math.AP2021★ 1 cited

Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density

Yatao Li, Qianyun Miao, Liutang Xue

The paper concerns with the global well-posedness issue of the 2D incompressible inhomogeneous Navier-Stokes (INS) equations with fractional dissipation and rough density. We first…

math.AP2021★ 1 cited

Global regularity of non-diffusive temperature fronts for the 2D viscous Boussinesq system

Dongho Chae, Qianyun Miao, Liutang Xue

In this paper we address the temperature patch problem of the 2D viscous Boussinesq system without heat diffusion term. The temperature satisfies the transport equation and the ini…

math.AP2020★ 2 cited

Global regularity for a 1D Euler-alignment system with misalignment

Qianyun Miao, Changhui Tan, Liutang Xue

We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied…

math.AP2019★ 2 cited

The Defocusing Energy-critical Klein-Gordon-Hartree Equation

Qianyun Miao, Jiqiang Zheng

In this paper, we study the scattering theory for the defocusing energy-critical Klein-Gordon equation with a cubic convolution $u_{tt} - Δ u + u + (∣ x ∣^{- 4} * ∣ u ∣^{2}) u = 0$ in the spatial…

math.AP2019

Everywhere differentiability of absolute minimizers for locally strongly convex and concave Hamiltonian $H (p) \in C^{0} (R^{n})$ with $n \geq 3$

Peng Fa, Qianyun Miao, Yuan Zhou

Suppose that $n \geq 3$ and $H (p) \in C^{0} (R^{n})$ is a locally strongly convex and concave Hamiltonian. We obtain the everywhere differentiability of all absolute minimizers for…

math.AP2019★ 2 cited

A quantative Sobolev regularity for absolute minimizers involving Hamiltonian $H (p) \in C^{0} (R^{2})$ in plane

Peng Fa, Qianyun Miao, Yuan Zhou

Suppose that $H \in C^{0} (R^{2})$ satisfies \begin{enumerate} \item[(H1)] $H$ is locally strongly convex and locally strongly concave in $\rr^2$, \item[(H2)] $H(0)=\min_{p\in…

math.AP2015★ 11 cited

Uniqueness of absolute minimizers for $L^\fz$-functionals involving Hamiltonians $H (x, p)$

Qianyun Miao, Changyou Wang, Yuan Zhou

For a bounded domain $U\subset\rn$, consider the $L^\fz$-functional involving a nonnegative Hamilton function $H:\overline U\times\rn\to [0,\fz)$. In this paper, we will establish…