scholarly journals On the Gevrey regularity of solutions to the 3D ideal MHD equations

2019 ◽  
Vol 39 (11) ◽  
pp. 6485-6506
Author(s):  
Feng Cheng ◽  
◽  
Chao-Jiang Xu ◽  
◽  
Keyword(s):  
Mhd Equations ◽  
Regularity Of Solutions ◽  
Gevrey Regularity ◽  
Ideal Mhd

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

scholarly journals Minimum quadratic helicity states

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
P. M. Akhmet’ev ◽  
S. Candelaresi ◽  
A. Y. Smirnov
Keyword(s):  
Mhd Equations ◽  
Ideal Mhd

Building on previous results on the quadratic helicity in magnetohydrodynamics (MHD) we investigate particular minimum helicity states. These are eigenfunctions of the curl operator and are shown to constitute solutions of the quasi-stationary incompressible ideal MHD equations. We then show that these states have indeed minimum quadratic helicity.

Positivity-preserving DG and central DG methods for ideal MHD equations

2013 ◽  
Vol 238 ◽  
pp. 255-280 ◽  
Author(s):  
Yue Cheng ◽  
Fengyan Li ◽  
Jianxian Qiu ◽  
Liwei Xu
Keyword(s):  
Mhd Equations ◽  
Positivity Preserving ◽  
Ideal Mhd ◽  
Dg Methods

Role of non-diagonal pressure tensor components in balance of magnetopause current sheet

2020 ◽  
Author(s):  
Egor Yushkov ◽  
Anton Artemyev ◽  
Anatoly Petrukovich
Keyword(s):  
Solar Wind ◽  
Current Sheet ◽  
Model Development ◽  
Mhd Equations ◽  
Pressure Tensor ◽  
Boundary Field ◽  
Ideal Mhd ◽  
Night Side ◽  
Rfbr Grant ◽  
Wind Characteristics

<p>We study the current sheet model separating a strong magnetic field area from the intense solar wind. We use the ideal MHD equations for ideas proposed by D. Nickeler and T. Wiegelmann to describe the transition region with plasma flows inclined to the boundary field. We show that balance in this case can be supported by nondiagonal components of modified pressure tensor. We discuss the possible application of the results to a description of the Earth’s night-side magnetopause boundary and study influence of solar wind characteristics on magnetopause current structure. We show problems that follow from ideal mhd-approach and from our assumptions about stationarity of two-dimensional CS on examples of magnetopause crossings by MMS mission. We speculate about further model development to day-side and magnetopause flanks application. This work is supported by the RFBR grant N 18-02-00218.</p>

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