Chapman's model for ozone concentration: earth`s slowing rotation effect in the atmospheric past

Abstract

Chapman&#39;s model for ozone concentration is studied. In this nonlinear model, the photodissociation coefficients for $O_{2}$ and $O_{3}$ are time-depending due to earth-rotation. From the Kapitsa&#39;s method, valid in the high frequency limit, we find the criterion for the existence of equilibrium solutions. These solutions are depending on the frequency, and require a rotation period $T$ which satisfies $T<T_{1}$ or $T>T_{2}$. Where the critical periods $T_{1}$ and $T_{2}$, with $T_{2}>T_{1}$, are a function of the parameters of the system (reaction rates and photodissociation coefficients). Conjectures respect to the retardation of the earth&#39;s rotation, due to friction, suggest that the criterion was not even verified in the atmospheric past.