Hall magnetohydrodynamics: Conservation laws and Lyapunov stability
- 1 May 1987
- journal article
- Published by AIP Publishing in Physics of Fluids
- Vol. 30 (5) , 1310-1322
- https://doi.org/10.1063/1.866246
Abstract
Hall electric fields produce circulating mass flow in confined ideal‐fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial‐value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions.Keywords
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