Alexandria Digital Research Library

Stochastic 2D Navier-Stokes Equation and Applications to 2D Turbulence

Author:
Karimi, Shahab
Degree Grantor:
University of California, Santa Barbara. Mathematics
Degree Supervisor:
Bjorn Birnir
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Mathematics and Mechanical engineering
Keywords:
Turbulence
Stochastic Navier-Stokes
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

We will consider the 2-dimensional Navier-Stokes equation for an incompressible fluid with periodic boundary condition, and with a random perturbation that is in the form of white noise in time and a deterministic perturbation due to the large deviation principle. Our ultimate goal is to find appropriate conditions on the initial data and the forcing terms so that global existence and uniqueness of a mild solution is guaranteed. We will use the Picard's iteration method to prove existence of local mild solution and then prove the existence of a maximal solution which then leads to global existence. The result is applied to the backward Kolmogorov-Obukhov energy cascade and the forward Kraichnan enstrophy cascade in 2D turbulence.

Physical Description:
1 online resource (63 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3zc82nn
ISBN:
9781339671901
Catalog System Number:
990046534420203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Shahab Karimi
File Description
Access: Public access
Karimi_ucsb_0035D_12950.pdf pdf (Portable Document Format)