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610 results on '"Cui, Xiufang"'

3. Vanishing viscosity limit for compressible magnetohydrodynamics equations with transverse background magnetic field

Author

Cui, Xiufang, Li, Shengxin, and Xie, Feng

Subjects
Mathematics - Analysis of PDEs
Abstract

We are concerned with the uniform regularity estimates and vanishing viscosity limit of solution to two dimensional viscous compressible magnetohydrodynamics (MHD) equations with transverse background magnetic field. When the magnetic field is assumed to be transverse to the boundary and the tangential component of magnetic field satisfies zero Neumann boundary condition, even though the velocity is imposed the no-slip boundary condition, the uniform regularity estimates of solution and its derivatives still can be achieved in suitable conormal Sobolev spaces in the half plane $\mathbb{R}^2_+$, and then the vanishing viscosity limit is justified in $L^\infty$ sense based on these uniform regularity estimates and some compactness arguments. At the same time, together with \cite{CLX21}, our results show that the transverse background magnetic field can prevent the strong boundary layer from occurring for compressible magnetohydrodynamics whether there is magnetic diffusion or not., Comment: 33 pages. arXiv admin note: text overlap with arXiv:2108.12969

Published
2022

12. Local $\varepsilon$-regularity criteria for the five dimensional stationary Navier-Stokes equations

Author

Cui, Xiufang

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper, we establish $\varepsilon$-regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations in both the unit ball $B_1$ and the unit half ball $B_1^+$, respectively, which improve previous results in [J. Math. Fluid Mech., 6(2004), pp 78--101] and [Comm. Pure Appl. Math., 41(1988), pp 437--458]. The proofs of the main results are based on an iteration argument, Campanato's method, and interpolation techniques.

Published
2021

15. Uniform regularity estimates and invisicid limit for the compressible non-resistive magnetohydrodynamics system

Author

Cui, Xiufang, Li, Shengxin, and Xie, Feng

Subjects
Mathematics - Analysis of PDEs
Abstract

We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to small viscosity coefficients. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in $L^\infty$ sense. It shows that the transverse magnetic field can prevent the boundary layers from occurring in some physical regime., Comment: 57 pages

Published
2021

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