Abstract:  A unifying approach for obtaining weighted L2 estimates for solutions to a class of multi-dimensional symmetric hyperbolic systems with constraints is presented. The main assumptions are that the system is isotropic and possesses a useful set of commuting vector fields. This type of estimate is an important step in obtaining dispersive estimates necessary for the construction of solutions to nonlinear problems. Global solutions to the equations of motion for incompressible nonlinear elasticity are constructed using these techniques.