Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables
Article first published online: 16 JUN 2010
Copyright © 2010 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 63, Issue 10, pages 1351–1361, October 2010
How to Cite
Majda, A. J. and Souganidis, P. E. (2010), Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables. Comm. Pure Appl. Math., 63: 1351–1361. doi: 10.1002/cpa.20337
- Issue published online: 20 JUL 2010
- Article first published online: 16 JUN 2010
- Manuscript Accepted: AUG 2009
The determination of the large-scale boundaries between moist and dry regions 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 moistening) 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. © 2010 Wiley Periodicals, Inc.