Conservation properties and potential systems of vorticitytype equations
Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergencetype conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lowerdegree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the GalasBogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lowerdegree conservation law is further shown to yield curltype conservation laws and determined potential equations in certain lowerdimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal timedependent MHD equations in 2+1 dimensions, are presented.
 Authors:

^{[1]}
 Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E6 (Canada)
 Publication Date:
 OSTI Identifier:
 22251027
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONSERVATION LAWS; EQUILIBRIUM; FUNCTIONS; MAGNETIC SURFACES; MAGNETOHYDRODYNAMICS; MAXWELL EQUATIONS; POTENTIALS; SCALARS; TIME DEPENDENCE; VECTORS; YIELDS