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Determining white noise forcing from Eulerian observations in the Navier-Stokes equation
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Hoang, Viet Ha, Law, Kody J. H. and Stuart, A. M. (2014) Determining white noise forcing from Eulerian observations in the Navier-Stokes equation. Stochastic Partial Differential Equations: Analysis and Computations, 2 (2). pp. 233-261. doi:10.1007/s40072-014-0028-4 ISSN 2194-0401.
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Official URL: http://dx.doi.org/10.1007/s40072-014-0028-4
Abstract
The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to, and the state of, a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D Navier-Stokes equation. The inverse problem is to make inference concerning the forcing, and possibly the initial condition, given noisy observations of the velocity field. We place a prior on the forcing which is in the form of a spatially-correlated and temporally-white Gaussian process, and formulate the inverse problem for the posterior distribution. Given appropriate spatial regularity conditions, we show that the solution is a continuous function of the forcing. Hence, for appropriately chosen spatial regularity in the prior, the posterior distribution on the forcing is absolutely continuous with respect to the prior and is hence well-defined. Furthermore, it may then be shown that the posterior distribution is a continuous function of the data. We complement these theoretical results with numerical simulations showing the feasibility of computing the posterior distribution, and illustrating its properties.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Stochastic Partial Differential Equations: Analysis and Computations | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 2194-0401 | ||||||||
Official Date: | 29 April 2014 | ||||||||
Dates: |
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Volume: | 2 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 233-261 | ||||||||
DOI: | 10.1007/s40072-014-0028-4 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 3 March 2017 |
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