A Semi Discrete Dynamical System for a 2D Dissipative Quasi Geostrophic Equation
This work provides theoretical foundations for numerical analysis of a geophysical fluid dynamics model, but is incremental as it extends known techniques to a specific discretization scheme.
The authors study a semi-discretization in time of the 2D dissipative quasi-geostrophic equation, proving existence, uniqueness, and regularity of solutions in the subcritical case, and establishing the existence of a global attractor for a specific source term.
A semi-discretization in time, according to a full implicit Euler scheme, for a 2D dissipative quasi geostrophic equation, is studied. We prove existence, uniqueness and regularity results of the solution to the predicted discretization, in the subcritical case for any initial data in $\dot{L}^2$. Hence, we define an infinite semi-discrete dynamical system, then we prove the existence and the regularity of the corresponding global attractor, for a source term $f$ in $\dot{L}^{p_α}$, for a fixed $p_α = \frac{2}{1-α} $.