A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 13, 2017
- Source ID
- 10.1515/ans-2016-6019
Entities
People
- Edriss Titi
- Michael S. Jolly
- Vincent R. Martinez
Organizations
- Indiana University
- Leverhulme Trust
- National Science Foundation
- Office of Naval Research
- Texas A&M Aggies football
- Tulane University of Louisiana