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
