We consider a model of quasigeostrophic turbulence that has proven useful in
theoretical studies of large scale heat transport and coherent structure formation in
planetary atmospheres and oceans. The model consists of a coupled pair of hyperbolic
PDEÂs with a forcing which represents domain-scale thermal energy source. Although
the use to which the model is typically put involves gathering information from very
long numerical integrations, little of a rigorous nature is known about long-time properties
of solutions to the equations. In the first part of my dissertation we define a
notion of weak solution, and show using Galerkin methods the long-time existence
and uniqueness of such solutions. In the second part we prove that the unique weak
solution found in the first part produces, via the inverse Fourier transform, a classical
solution for the system. Moreover, we prove that this solution is analytic in space
and positive time.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/3164 |
| Date | 12 April 2006 |
| Creators | Onica, Constantin |
| Contributors | Foias, Ciprian |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 317327 bytes, electronic, application/pdf, born digital |
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