Qualitative Theory of Rotating Boussinesq & Quasigeostrophic Equations

Qualitative Theory of Rotating Boussinesq & Quasigeostrophic Equations

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The author elucidates in a concrete way dynamical challenges concerning approximate inertial manifolds (AIMS), i.e., globally invariant, exponentially attracting, finite-dimensional smooth manifolds, for nonlinear dynamical systems on Hilbert spaces. The goal of this theory is to prove the basic theorem of approximation dynamics, wherein it is shown that there is a fundamental connection between the order of the approximating manifold and the well-posedness and long-time dynamics of the rotating Boussinesq and quasigeostrophic equations. The author discusses recent progress in analytical and n...