One class of MHD equations: Conservation laws and exact solutions

DOI10.1111/sapm.12616zbMath1528.35126OpenAlexW4383550779MaRDI QIDQ6091780

Unnamed Author, Sergey V. Meleshko

Publication date: 27 November 2023

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/sapm.12616

zbMATH Keywords

conservation lawexact solutionsLagrangian coordinatesNoether's theoremLie point symmetriesMHD equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Solutions to PDEs in closed form (35C05) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60) Methods of ordinary differential equations applied to PDEs (35A24)

Cites Work

• Natural curvilinear coordinates for ideal MHD equations. Non-stationary flows with constant total pressure
• A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
• Magnetohydrodynamics and fluid dynamics: action principles and conservation laws
• Exact solutions of stationary equations of ideal magnetohydrodynamics in the natural coordinate system
• Some exact solutions of the ideal MHD equations through symmetry reduction method
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Exact solutions to the ideal magneto-gas-dynamics equations through Lie group analysis and substitution principles
• Group classification of the two‐dimensional magnetogasdynamics equations in Lagrangian coordinates
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