Energy decay of solutions to the Boussinesq, primitive, and planetary geostrophic equations
The authors study in the whole \(\mathbb{R}^3\) the long-time behaviour of the energy of solutions to the basic equations modelling atmospheric and oceanic flows. More precisely, under consideration are Boussinesq, primitive, and planetary geostrophic equations. Using the Fourier splitting method, it is shown that the asymptotic long-time behaviour depends on the type of data, and on the number of non-zero damping constants in the equations. In several particular cases, the authors establish an algebraic rate of decay or ocsillating behaviour for \(t\to\infty\).
scientific article; zbMATH DE number 1334720