TY - JOUR
T1 - Rearrangements of vector valued functions, with application to atmospheric and oceanic flows
AU - Douglas, R. J.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1998/7
Y1 - 1998/7
N2 - 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].
AB - 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].
KW - Generalized solution
KW - Rearrangement of functions
KW - Semigeostrophic
KW - Variational problems
UR - http://www.scopus.com/inward/record.url?scp=0032384448&partnerID=8YFLogxK
U2 - 10.1137/S003614109628216X
DO - 10.1137/S003614109628216X
M3 - Article
AN - SCOPUS:0032384448
SN - 0036-1410
VL - 29
SP - 891
EP - 902
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 4
ER -