Abridged Continuous Data Assimilation for the 2D Navier-Stokes Equations Utilizing Measurements of Only One Component of the Velocity Field

abstract

• 2015, Springer Basel. We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional NavierStokes equations employing coarse mesh measurements of only one component of the velocity field. This algorithm can be implemented with a variety of finitely many observables: low Fourier modes, nodal values, finite volume averages, or finite elements. We provide conditions on the spatial resolution of the observed data, under the assumption that the observed data is free of noise, which are sufficient to show that the solution of the algorithm approaches, at an exponential rate asymptotically in time, to the unique exact unknown reference solution, of the 2D NavierStokes equations, associated with the observed (finite dimensional projection of) velocity.

authors

• Titi, Edriss

published proceedings

• JOURNAL OF MATHEMATICAL FLUID MECHANICS

altmetric score

• 0.5

author list (cited authors)

• Farhat, A., Lunasin, E., & Titi, E. S.

citation count

• 50

complete list of authors

• Farhat, Aseel||Lunasin, Evelyn||Titi, Edriss S

publication date

• March 2016

publisher

• Springer Nature  Publisher

published in

• Journal of Mathematical Fluid Mechanics  Journal

keywords

• Coarse Mesh Measurements Of Only One Component Of The Velocity Field
• Continuous Data Assimilation
• Downscaling
• Feedback Control
• Navier-stokes Equations
• Nudging
• Signal Synchronization
• Volume Elements And Nodes

Digital Object Identifier (DOI)

• 10.1007/s00021-015-0225-6

start page

• 1

end page

• 23

volume

• 18

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00021-015-0225-6