85 citations · 234 across the 19 of their papers we have counts for
19 papers
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 dimensions with unidirectional flows and strongly singular communication protocols for $α…
Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc
Taoufik Hmidi, Liutang Xue, Zhilong Xue
In this paper we address the existence of time periodic solutions for the generalized inviscid SQG equation in the unit disc with homogeneous Dirichlet boundary condition when $α\i…
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…
On the regularity of temperature fronts for the 3D viscous Boussinesq system
Omar Lazar, Yatao Li, Liutang Xue
We study the temperature front problem for the 3D viscous Boussinesq equation. We prove that the (, ) and regularity of a temperature fron…
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…
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…
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…
Boussinesq system with measure forcing
Piotr B. Mucha, Liutang Xue
We address a question concerning the issue of existence to a Boussinesq type system with a heat source. The problem is studied in the whole two dimensional plane and the heat sourc…
Between homogeneous and inhomogeneous Navier-Stokes systems: the issue of stability
Piotr B. Mucha, Liutang Xue, Xiaoxin Zheng
We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with c…
Regularity results for a class of generalized surface quasi-geostrophic equations
Omar Lazar, Liutang Xue
We show a global existence result of weak solutions for a class of generalized Surface Quasi-Geostrophic equation in the inviscid case. We also prove the global regularity of such…
On the Differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion
Liutang Xue, Zhuan Ye
We investigate the differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion at either supercritical or critical type cases. Under the suitable cond…
On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion
Changxing Miao, Liutang Xue
In this paper we address the regularity issues of drift-diffusion equation with nonlocal diffusion, where the diffusion operator is in the realm of stable-type Lévy operator and th…
On the locally self-similar singular solutions for the incompressible Euler equations
Liutang Xue
In this paper we consider the locally backward self-similar solutions for the Euler system, and focus on the case that the possible nontrivial velocity profiles have non-decaying a…
Discretely self-similar singular solutions for the incompressible Euler equations
Liutang Xue
In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymp…
On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation dynamics
Dong Li, Changxing Miao, Liutang Xue
In this paper we consider a 2D nonlinear and nonlocal model describing the dynamics of the dislocation densities. We prove the local well-posedness of strong solution to this syste…
Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing
M. Cannone, C. Miao, L. Xue
We consider the 2D quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we…
On the regularity of a class of generalized quasi-geostrophic equations
Changxing Miao, Liutang Xue
In this article we consider the following generalized quasi-geostrophic equation \partial_tθ+ u\cdot\nabla θ+ νΛ^βθ=0, \quad u= Λ^α\mathcal{R}^\botθ, \quad x\in\mathbb{R}^2, where…
On the global well-posedness of a class of Boussinesq- Navier-Stokes systems
Changxing Miao, Liutang Xue
In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^αu &= θe_{2} \partial_{t}θ+u\cdot\nabla θ+ |D|^βθ&=0 \quad wi…
Global Wellposedness for a Modified Critical Dissipative Quasi-Geostrophic Equation
Changxing Miao, Liutang Xue
In this paper we consider the following modified quasi-geostrophic equation \partial_{t}θ+u\cdot\nablaθ+ν|D|^αθ=0, \quad u=|D|^{α-1}\mathcal{R}^{\bot}θ,\quad x\in\mathbb{R}^2 with…