73 citations · 113 across the 10 of their papers we have counts for
11 papers
Analysis on Tollmien-Schlichting wave in the Prandtl-Hartmann Regime
Cheng-Jie Liu, Tong Yang, Zhu Zhang
In this paper, we study the instability induced by the Tollmien-Schlichting wave governed by the MHD system in the Prandtl-Hartmann regime. The interaction of the inviscid mode and…
Validity of Prandtl expansions for steady MHD in the Sobolev framework
Cheng-Jie Liu, Tong Yang, Zhu Zhang
This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary…
Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces
Cheng-Jie Liu, Dehua Wang, Feng Xie +1
In this paper, we are concerned with the magnetic effect on the Sobolev solvability of boundary layer equations for the 2D incompressible MHD system without resistivity. The MHD bo…
Local-in-time well-posedness for Compressible MHD boundary layer
Huang Yongting, Liu Cheng-Jie, Yang Tong
In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane, w…
Justification of Prandtl Ansatz for MHD boundary layer
Cheng-Jie Liu, Feng Xie, Tong Yang
As a continuation of \cite{LXY}, the paper aims to justify the high Reynolds numbers limit for the MHD system with Prandtl boundary layer expansion when no-slip boundary condition…
MHD boundary layers theory in Sobolev spaces without monotonicity. I. well-posedness theory
Cheng-Jie Liu, Feng Xie, Tong Yang
We study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl type equations that are derived from the incompressible MHD…
Well-posedness of thermal layer equations for inviscid compressible flows
Cheng-Jie Liu, Ya-Guang Wang, Tong Yang
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when t…
Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay
Cheng-Jie Liu, Tong Yang
Motivated by the paper by D. Gerard-Varet and E. Dormy [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal va…
Global existence of weak solutions to the three-dimensional Prandtl equations with A special structure
Cheng-Jie Liu, Ya-Guang Wang, Tong Yang
The global existence of weak solutions to the three space dimensional Prandtl equations is studied under some constraint on its structure. This is a continuation of our recent stud…
On the ill-posedness of the Prandtl equations in three space dimensions
Cheng-Jie Liu, Ya-Guang Wang, Tong Yang
In this paper, we give an instability criterion for the Prandtl equations in three space variables, which shows that the monotonicity condition of tangential velocity fields is not…
A well-posedness theory for the Prandtl equations in three space variables
Cheng-Jie Liu, Ya-Guang Wang, Tong Yang
The well-posedness of the three space dimensional Prandtl equations is studied under some constraint on its flow structure. It reveals that the classical Burgers equation plays an…