论二维非理想磁流体力学简波的存在

Gaurav, L. P. Singh
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摘要

摘要 本文采用一种称为特征分解的方法来说明非理想磁流体力学系统中二维可压缩流动存在简单波。本文考虑了稳态和伪稳态磁流体力学系统,并给出了这两个系统中流动方程的特征分解。这种分解确保了所考虑的系统在恒定状态区域附近存在一个简单波。此外,我们还将这一结果扩展为特征分解在伪稳态中的应用,并通过沿伪流特征将涡度和熵取为常数,证明了全磁流体力学系统中简波的存在。这些结果扩展了 Courant 和 Friedrichs 针对可还原系统提出的基本定理(R. Courant 和 K. O. Friedrichs,《超音速流和冲击波》,纽约,Interscience 出版社,1948 年,第 464 页)。Li 等人针对理想气体开展了一项激励性工作("Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations," Commun.Math.Phys.267, no. 1, pp.物理》,第 55 卷,第 9 期,第 093103-093112 页,2014 年],[M.Zafar, "A note on characteristic decomposition for two-dimensional euler system in van der waals fluids," Int. J. Non-Linear Mech.J. Non-Linear Mech., vol. 86, pp.]
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On the existence of simple waves for two-dimensional non-ideal magneto-hydrodynamics
Abstract In this article, a method called characteristic decomposition is used to show the presence of simple waves for the two-dimensional compressible flow in a non-ideal magneto-hydrodynamics system. Here, a steady and pseudo-steady state magneto-hydrodynamics system is considered, and we provide a characteristic decomposition of the flow equations in both systems. This decomposition ensures the presence of a simple wave adjacent to a region of constant state for the system under consideration. Further, this result is extended as an application of the characteristic decomposition in a pseudo-steady state, and we prove the existence of a simple wave in a full magneto-hydrodynamics system by taking the vorticity and the entropy to be constant along the pseudo-flow characteristics. These results extend the fundamental theorem proposed by Courant and Friedrichs for a reducible system (R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, New York, Interscience Publishers, Inc., 1948, p. 464). A motivational work was carried out for an ideal gas by Li et al. (“Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations,” Commun. Math. Phys. Math. Phys., vol. 267, no. 1, pp. 1–12, 2006) and for a non-ideal gas by Zafar and Sharma (“Characteristic decomposition of compressible Euler equations for a non-ideal gas in two-dimensions,” J. Math. Phys., vol. 55, no. 9, pp. 093103–093112, 2014], [M. Zafar, “A note on characteristic decomposition for two-dimensional euler system in van der waals fluids,” Int. J. Non-Linear Mech., vol. 86, pp. 33–36, 2016].
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