Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables

Andrew J. Majda; Panagiotis E. Souganidis

doi:10.1002/cpa.20337

Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables

Andrew J. Majda, Panagiotis E. Souganidis

Research output: Contribution to journal › Article › peer-review

Abstract

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 simplfied 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.

Original language	English (US)
Pages (from-to)	1351-1361
Number of pages	11
Journal	Communications on Pure and Applied Mathematics
Volume	63
Issue number	10
DOIs	https://doi.org/10.1002/cpa.20337
State	Published - Oct 2010

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.20337

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abstract = "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 simplfied 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.",

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AB - 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 simplfied 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.

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Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables

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