A new approach to constrained systems with a convex extension

Abstract

Systems S of N partial differential equations are considered, with M differential constraints and satisfying a convex supplementary conservation law. When M = 0, it is well known that these systems assume the symmetric hyperbolic form if the components of the mean field are taken as independent variables. To extend this property to the case , a new system is here proposed with M supplementary variables such that the solutions of with are those of the system S. Moreover S can be expressed in the symmetric hyperbolic form. This methodology is tested by applying it to the equations of the superfluid, modified from the classical Landau's formulation.