THE EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR PRECIPITATION FRONTS: A NOVEL HYPERBOLIC FREE BOUNDARY PROBLEM IN SEVERAL SPACE VARIABLES

Abstract. The determination of the large scale boundaries between moist and dry re-gions is an important problem in contemporary meteorology. These phenomena have been addressed recently in a simplified tropical climate model through a novel hyperbolic free boundary formulation yielding three families (drying, slow moistening, and fast moisten-ing) of precipitation fronts. The last two wave types violate Lax’s shock inequalities yet are robustly realized. This formal hyperbolic free boundary problem is given here a rigorous mathematical basis by establishing the existence and uniqueness of suitable weak solutions arising in the zero relaxation limit. A new L2-contraction estimate is also established at positive relaxation values. The goal here is to prove the existence and uniqueness of weak solutions to a novel hyper-bolic free boundary value problem in several space variables that has emerged recently in the analysis of precipitation fronts in the large scale tropical atmosphere ([FMP], [SM], [PFM], [KM1], [KM2]). Precipitation fronts are the boundaries between the zones of extremel