Rearrangements of vector valued functions, with application to atmospheric and oceanic flows

R. J. Douglas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)

Abstract

This paper establishes the equivalence of four definitions of two vector valued functions being rearrangements. Properties of the monotone rearrangement of a vector valued function are used to show existence and uniqueness of the minimizer of an energy functional arising from the semigeostrophic equations, a model for atmospheric and oceanic flow. At each fixed time solutions are shown to be equal to the gradient of a convex function, verifying the conjecture of Cullen, Norbury, and Purser [SIAM J. Appl. Math., 51 (1991). pp. 20-31].

Original languageEnglish
Pages (from-to)891-902
Number of pages12
JournalSIAM Journal on Mathematical Analysis
Volume29
Issue number4
DOIs
Publication statusPublished - Jul 1998

Keywords

  • Generalized solution
  • Rearrangement of functions
  • Semigeostrophic
  • Variational problems

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