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 $M≠ 0$, a new system $S^*$ is here proposed with M supplementary variables $x_A$ such that the solutions of $S^*$ with $x_A = 0$ 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.