A data assimilation algorithm for the subcritical surface quasi-geostrophic equation

In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this boundary, a scalar unknown (buoyancy or surface temperature of the fluid) satisfies the surface quasi-geostrophic equation. The feedback nudging is done on this two-dimensional model, yet ultimately synchronizes the streamfunction of the three-dimensional flow. The main analytical difficulties are due to the presence of a nonlocal dissipative operator in the surface quasi-geostrophic equation. This is overcome by exploiting a suitable partition of unity, the modulus of continuity characterization of Sobolev space norms, and the Littlewood–Paley decomposition to ultimately establish various boundedness and approximation-of-identity properties for the observation operators.


Publication Date:
Jan 13 2017
Date Submitted:
Aug 10 2018
Pagination:
167-192
ISSN:
1536-1365
Citation:
Advanced Nonlinear Studies
17
1
Note:
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 Record created 2018-08-10, last modified 2019-04-03


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