期刊
ADVANCED NONLINEAR STUDIES
卷 17, 期 1, 页码 167-192出版社
DE GRUYTER POLAND SP Z O O
DOI: 10.1515/ans-2016-6019
关键词
Data Assimilation; Nudging; Surface Measurements; Quasi-Geostrophic and Surface; Quasi-Geostrophic Equation; Fractional Poincare Inequalities
资金
- NSF [DMS-1418911, DMS-1109640, DMS-1109645]
- Leverhulme Trust [VP12015-036]
- ONR [N00014-15-1-2333]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1440415, 1418911] Funding Source: National Science Foundation
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.
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