Symmetry Analysis of the Two-Dimensional Stationary Magnetogasdynamics Equations With Coriolis Force in Lagrangian Coordinates

Abstract

The paper focuses on symmetry analysis of the two-dimensional stationary magnetogasdynamics equations with Coriolis force in Lagrangian coordinates. This involves the identification of equivalence transformations and the Lie algebra admitted by the equations, and its extensions for various forms of magnetic fields and Coriolis parameter, as well as the construction of group foliations. A considerable part of the work is devoted to group foliations of the magnetogasdynamics equations, extending to the nonstationary isentropic case. The group foliations' approach is typically applied to equations admitting infinite-dimensional groups of transformations, thereby facilitating the simplification of their subsequent analysis. The results obtained in this study generalize previously known findings for the two-dimensional shallow water equations and stationary gas dynamics equations in Lagrangian coordinates. Utilizing the constructed group foliations, invariant solutions are derived for particular forms of the entropy, illustrating the potential for further investigation in this area.