Linearized Analysis of One-Dimensional Magnetohydrodynamic Flows

Interaction of waves in one-dimensional dusty gas flow

“…In most of the literature, only approximate analytical or numerical solutions are discussed. In this context, it is worth to mention the contributions made by many authors like Hunter and Ali [4], Gunderson [5], He and Moodie [6], Whitham [7], Moodie et al [8], Arora and Sharma [9], Arora [10], Fusco [11].…”

Solution of the Riemann Problem in magnetogasdynamics

“…It is also an important example of the hyperbolic system's theory. The governing system of magnetogasdynamics is highly non-linear and complicated, it is necessary to study various simplified models [16][17][18] i.e. flow of magnetic and velocity fields are orthogonal everywhere.…”

On the non-resistive limit and the magnetic boundary-layer for one-dimensional compressible magnetohydrodynamics

“…Due to the complicated structure of multi-dimensional equations, instead of (1.1) and (1.3), in this paper we shall consider the simplest one-dimensional equations (cf. [12]): where the pressure P (ρ) obeys the γ-law (1.2) and λ = 2µ + λ ′ . Indeed, assume that the MHD flow is moving only in the longitudinal direction x and uniform in the transverse directions (y, z).…”

“…Due to (1.5) 1 , it holds that 12) and hence, the first term on the right-hand side of (2.11) can be estimated as follows.…”

“…Due to the complicated structure of multi-dimensional equations, instead of (1.1) and (1.3), in this paper we shall consider the simplest one-dimensional equations (cf. [12]):…”