Qianyun Miao

activity

20222024

collaborators

4 papers

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.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…

A nonlinear Calderón-Zygmund L2-theory for the Dirichlet problem involving −∣Du∣γΔpN​u=f

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

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

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

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

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