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

作者：Farhat Aseel; Lunasin Evelyn; Titi Edriss S

来源：Journal of Mathematical Fluid Mechanics, 2016, 18(1): 1-23.

DOI：10.1007/s00021-015-0225-6

• Navier-Stokes equations
• continuous data assimilation
• signal synchronization
• volume elements and nodes
• coarse mesh measurements of only one component of the velocity field
• feedback control
• nudging
• downscaling

We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional Navier-Stokes 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 Navier-Stokes equations, associated with the observed (finite dimensional projection of) velocity.

• 出版日期2016-3
• 单位中国人民解放军海军大连舰艇学院