40 citations · 194 across the 24 of their papers we have counts for
25 papers
A wall-law approximation for Jeffery-Hamel flows in rough wedges
Zijin Li, Xinghong Pan
We study the two-dimensional stationary Navier-Stokes equations in an unbounded wedge with small rough perturbations of its angular boundaries. The Jeffery-Hamel flow in the corres…
Globally analytical solutions of the compressible Oldroyd-B model without retardation
Xinghong Pan
In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a non-vacuum equilibrium in $(n=2,…
Long-time existence of Gevrey-2 solutions to the 3D Prandtl boundary layer equations
Xinghong Pan, Chao-Jiang Xu
For the three dimensional Prandtl boundary layer equations, we will show that for arbitrary and sufficiently small , the lifespan of the Gevrey-2 solution is at least of siz…
Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition
Zijin Li, Xinghong Pan, Jiaqi Yang
In this paper, we will solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, un…
Finite speed axially symmetric Navier-Stokes flows passing a cone
Zijin Li, Xinghong Pan, Xin Yang +3
Let be the exterior of a cone inside a ball, with its altitude angle at most in , which touches the axis at the origin. For any initial value $v_0 = v…
On Leray's problem in an infinite-long pipe with the Navier-slip boundary condition
Zijin Li, Xinghong Pan, Jiaqi Yang
The original Leray's problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe, which approach to the Poiseuill…
Global tangentially analytical solutions of the 3D axially symmetric Prandtl equations
Xinghong Pan, Chao-Jiang Xu
In this paper, we will prove the global existence of solutions to the three dimensional axially symmetric Prandtl boundary layer equations with small initial data, which lies in $H…
Characterization of smooth solutions to the Navier-Stokes equations in a pipe with two types of slip boundary conditions
Zijin Li, Xinghong Pan, Jiaqi Yang
Smooth solutions of the stationary Navier-Stokes equations in an infinitely long pipe, equipped with the Navier-slip or Navier-Hodge-Lions boundary condition, are considered in thi…
A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang
Qi S. Zhang
In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property fo…
One component regularity criteria for the axially symmetric MHD-Boussinesq system: criteria on the swirl component of the velocity
Zijin Li, Xinghong Pan
In this paper, we consider regularity criteria of a class of 3D axially symmetric MHD-Boussinesq systems without magnetic resistivity or thermal diffusivity. Under some Prodi-Serri…
Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping
Xinghong Pan
In this paper, the smooth solution of the physical vacuum problem for the one dimensional compressible Euler equations with time-dependent damping is considered. Near the vacuum bo…
Time analyticity for inhomogeneous parabolic equations and the Navier-Stokes equations in the half space
Hongjie Dong, Xinghong Pan
We prove the time analyticity for weak solutions of inhomogeneous parabolic equations with measurable coefficients in the half space with either the Dirichlet boundary condition or…
Asymptotic properties of generalized D-solutions to the stationary axially symmetric Navier-Stokes equations
Zijin Li, Xinghong Pan
In this paper, we derive asymptotic properties of both the velocity and the vorticity fields to the 3-dimensional axially symmetric Navier-Stokes equations at infinity under the ge…
Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data
Xinghong Pan
In this paper, we will show that solutions of the three-dimensional non-resistive and non-diffusive MHD-Boussinesq system are globally regular if the initial data is axisymmetric a…
Liouville theorem of axially symmetric Navier-Stokes equations with growing velocity at infinity
Xinghong Pan, Zijin Li
In the paper \cite{KNSS:1}, the authors make the following conjecture: {\it any bounded ancient mild solution of the 3D axially symmetric Navier-Stokes equations is constant.} And…
Global existence in critical spaces for non Newtonian compressible viscoelastic flows
Xinghong Pan, Jiang Xu, Yi Zhu
We are interested in the multi-dimentional compressible viscoelastic flows of Oldroyd type, which is one of non-Newtonian fluids exhibiting the elastic behavior. In order to captur…
On the Vanishing of some D-solutions to the Stationary Magnetohydrodynamics System
Zijin Li, Xinghong Pan
In this paper, we study the stationary magnetohydrodynamics system in . We prove trivialness of D-solutions (the velocity field and the magnetic f…
Decay and vanishing of some D-solutions of the Navier-Stokes equations
Bryan Carrillo, Xinghong Pan, Qi S. Zhang +1
An old problem since Leray \cite{Le:1} asks whether homogeneous D solutions of the 3 dimensional Navier-Stokes equation in or some noncompact domains are 0. In this…
Some Remarks on Regularity Criteria of Axially Symmetric Navier-Stokes Equations
Zijin Li, Xinghong Pan
Two main results will be presented in our paper. First, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a supercritical assumptio…
Blow up of solutions for semilinear wave equations with noneffective damping
Zijin Li, Xinghong Pan
In this paper, we study the finite-time blow up of solutions to the following semilinear wave equation with time-dependent damping \[ \partial_t^2u-Δu+\fracμ{1+t}\partial_tu=|u|^p…
Decay and vanishing of some axially symmetric D-solutions of the Navier-Stokes equations
Bryan Carrillo, Xinghong Pan, Qi S. Zhang
We study axially symmetric D-solutions of the 3 dimensional Navier-Stokes equations. The first result is an a priori decay estimate of the velocity for general domains. The second…
Global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows
Xinghong Pan, Jiang Xu
This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space with any $n…
Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping
Xinghong Pan
We study the isentropic Euler equations with time-dependent damping, given by . Here, are two non-negative constants to describe the decay rate of damping…
Remarks on 1-D Euler Equations with Time-Decayed Damping
Xinghong Pan
We study the 1-d isentropic Euler equations with time-decayed damping \begin{equation} \left\{ \begin{aligned} &\partial_t ρ+\partial_x(ρu)=0, \\ &\partial_t(ρu)+ \partial_x(ρu^2)+…