Stochastic 2D Navier-Stokes Equation and Applications to 2D Turbulence
- 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:
- Mechanical engineering and Mathematics
- Keywords:
- Stochastic Navier-Stokes,
Turbulence - Genres:
- Online resources and Dissertations, Academic
- 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
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:10103624
- ARK:
- ark:/48907/f3zc82nn
- ISBN:
- 9781339671901
- Catalog System Number:
- 990046534420203776
- Copyright:
- Shahab Karimi, 2016
- Rights:
- In Copyright
- Copyright Holder:
- Shahab Karimi
File | Description |
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Access: Public access | |
Karimi_ucsb_0035D_12950.pdf | pdf (Portable Document Format) |