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 journalArticle

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 languageEnglish (US)
Pages (from-to)1351-1361
Number of pages11
JournalCommunications on Pure and Applied Mathematics
Volume63
Issue number10
DOIs
StatePublished - Oct 2010

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Free Boundary Problem
Weak Solution
Wetting
Existence and Uniqueness
Suitable Weak Solutions
Relaxation Limit
Climate models
Meteorology
Climate Models
Drying
Violate
Free Boundary
Shock
Contraction
Formulation
Zero
Estimate
Family

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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