Hall magnetohydrodynamics: Conservation laws and Lyapunov stability

Journal Article · Fri May 01 04:00:00 EDT 1987 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.866246· OSTI ID:6633730

Holm, D D

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.

• Research Organization: Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, MS B284, Los Alamos, New Mexico 87545
• OSTI ID: 6633730
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 30:5; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

640430* -- Fluid Physics-- Magnetohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONSERVATION LAWS
FLUID MECHANICS
HALL EFFECT
HAMILTONIANS
HYDRODYNAMICS
LYAPUNOV METHOD
MAGNETOHYDRODYNAMICS
MASS TRANSFER
MATHEMATICAL OPERATORS
MECHANICS
NONLINEAR PROBLEMS
PLASMA
PLASMA DRIFT
QUANTUM OPERATORS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS