Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Data Assimilation with Stochastically Noisy Data   We analyze the performance of a data-assimilation algorithm based on a linear
feedback control when used with observational data that contains measurement
errors. Our model problem consists of dynamics governed by the two-dimension
incompressible Navier-Stokes equations, observational measurements given by
finite volume elements or nodal points of the velocity field and measurement
errors which are represented by stochastic noise. Under these assumptions, the
data-assimilation algorithm consists of a system of stochastically forced
Navier-Stokes equations. The main result of this paper provides explicit
conditions on the observation density (resolution) which guarantee explicit
asymptotic bounds, as the time tends to infinity, on the error between the
approximate solution and the actual solutions which is corresponding to these
measurements, in terms of the variance of the noise in the measurements.
Specifically, such bounds are given for the the limit supremum, as the time
tends to infinity, of the expected value of the $L^2$-norm and of the $H^1$
Sobolev norm of the difference between the approximating solution and the
actual solution. Moreover, results on the average time error in mean are
stated.

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio