Solution globale de l’équation de coagulation des gouttelettes en chute avec le vent horizontal

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

“…In [17] has been introduced a model of motion of the air and the phase transition of water in the three states in the atmosphere. Since then, many papers have been produced in relation to this model (see for example [15], [3] [1], [18], [19], etc.). In particular, in the paper [15], under some suitable conditions, has been proved the existence and the uniqueness of the stationary solution for the equation of water droplets, without taking into account the condensation or evaporation process, assuming a domain with two spatial dimensions and a horizontal constant wind.…”

“…In particular, in the paper [15], under some suitable conditions, has been proved the existence and the uniqueness of the stationary solution for the equation of water droplets, without taking into account the condensation or evaporation process, assuming a domain with two spatial dimensions and a horizontal constant wind. Moreover in [3] has been shown, under weak assumptions, the global existence and uniqueness of the solution for the same equation, without taking into account the wind, on a domain with one spatial dimension. On the other hand, in the paper [19] has been proved the existence and the uniqueness, in W 1,∞ , of the local solution of an IBVP for the hyperbolic part of the model introduced in [17], on a strip bounded by two horizontal planes with the boundary condition such that rain fall from the strip.…”