Abstract
Foias–Prodi estimates for the 2D Navier–Stokes equations
We consider the Foias-Prodi estimates as a tool to investigate the asymptotic behavior of the 2D Navier-Stokes equations.
First, we revise the result in the deterministic setting. Then we consider the stochastic Navier-Stokes equations.
With an additive noise the uniqueness of the invariant measure by means of coupling technique has been proved by Glatt-Holtz, Mattingly and Richards (2017). This is based on pathwise Foias-Prodi estimates.
We show how to modify this technique when the noise is multiplicative, requiring the Foias-Prodi estimates in expectation.
Finally, if time permits, we show how to use this strategy to deal with the Continuous Data Assimilation (Azouani-Olson-Titi algorithm) to 2D stochastic Navier-Stokes equations.
The talk is based on joint work with M. Zanella, and in the last part also with H. Bessaih and O. Landoulsi.