Accuracy and stability of the continuous-time<br/><br/>3DVAR-filter for 2D Navier-Stokes Equation

Wednesday, October 24, 2012 - 9:00am - 9:50am
Keller 3-180
Dirk Blömker (Universität Augsburg)
We consider a noisy observer
for an unknown solution u(t) of a deterministic model.
The observer is a stochastic model similar to the original one,
and it arises as a limit of frequent observations in filtering.
Here noisy observations of the low Fourier modes of u(t)
together with knowledge of the deterministic model are used to track
the unknown solution u(t).

In this talk
as an example we discuss the simple 3DVAR-filter and the deterministic
2D-Navier Stokes equation.
We establish stability and accuracy of the filter by studying
this for the stochastic PDE describing the observer.

For stability one has to show that solutions of the observer starting from
different initial conditions converge exponentially fast towards each other.
This would also imply that the random attractor of the observer
is at most a single random point.

Accuracy means that any solution of the observer converges
exponentially fast to a small neighbourhood of the unknown solution u(t).
In terms of random attractors one has to verify that the whole attractor
is close to u(t).

Joint work with Andrew Stuart, Kody Law, and Konstantinos Zygalakis
MSC Code: