Hanane Belhireche | Searcharxiv

arXiv2016

Equation system describing the radiation intensity and the air motion with the water phase transition

In this paper we consider the equation system describing the motion of the air and the variation of the radiation intensity and the quantity of water droplets in the air, including also the process of water phase transition. Under a suitable condition we prove the existence and uniqueness of the local solution. By eliminating the approximation by regularization of vapor density and by including the equation of radiation, this result improves previous ones.

math.AP↗

arXiv2015

Global solution for the coagulation equation of water droplets in atmosphere between two horizontal planes

In this paper we give a global existence and uniqueness theorem for an initial and boundary value problem (IBVP) relative to the coagulation equation of water droplets and we show the convergence of the global solution to the stationary solution. The coagulation equation is an integro-differential equation that describes the variation of the density $σ$ of water droplets in the atmosphere. Furthermore, IBVP is considered on a strip limited by two horizontal planes and its boundary condition is such that rain fall from the strip. To obtain this result of global existence of the solution $σ$ in the space of bounded continuous functions, through the method of characteristics, we assume bounded continuous and small data, whereas the vector field, besides being bounded continuous, has $W^{1,\infty}-$ regularity in space.

math.AP↗