The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions...
We explore the optimal time path of carbon sequestration and carbon abatement in stabilizing
CO₂ levels under uncertainty of climate impacts. Using a two-period sequential decision making
model, we analytically derive optimal rates for the two control variables, abatement and
sequestration rates. Uncertainty is assumed to affect the desired future...