Local existence results for the generalized inverse of the vorticity equation in the plane

Carl R. Hagelberg, Andrew F. Bennett, Donald Jones

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We prove the finite-time existence of a solution to the Euler-Lagrange equations corresponding to the necessary conditions for minimization of a functional defining varational a assimilation of observational data into the two-dimensional, incompressible Euler equations. The data are given by linear functionals acting on the space of functions representing vorticity. The d data are sparse and avilable on a fixed space-time domain. The objective of the data assimilation is to obtain an estimate of the vorticity which minimizes a cost functional and is anlogous to a distributed parameter control problem. The cost functional i is the sum of a weighted squared error in the dynamics, the initial condition, and in the misfit to the observed data. Vorticity estimates which minimize the cost functional are obtained by solving the corresponding system of Euler-Lagrange Equations. The Euler-Lagrange system is a coupled two-point boundary value problem in time. An application of the Schauder fixed-point theorem establishes the existence of a least one solution to the system. Iterative methods for generating solutions have proven useful in applications in meterology and oceanography.

Original languageEnglish (US)
Pages (from-to)437-454
Number of pages18
JournalInverse Problems
Volume12
Issue number4
DOIs
StatePublished - Aug 1996

Fingerprint

vorticity equations
Local Existence
Generalized Inverse
Vorticity
vorticity
Existence Results
Euler-Lagrange equation
assimilation
costs
Euler-Lagrange Equations
oceanography
Oceanography
Costs
Euler equations
estimates
Iterative methods
Minimise
Incompressible Euler Equations
boundary value problems
functionals

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Local existence results for the generalized inverse of the vorticity equation in the plane. / Hagelberg, Carl R.; Bennett, Andrew F.; Jones, Donald.

In: Inverse Problems, Vol. 12, No. 4, 08.1996, p. 437-454.

Research output: Contribution to journalArticle

Hagelberg, Carl R. ; Bennett, Andrew F. ; Jones, Donald. / Local existence results for the generalized inverse of the vorticity equation in the plane. In: Inverse Problems. 1996 ; Vol. 12, No. 4. pp. 437-454.
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