Solution stationnaire de l'équation de coagulation de gouttelettes en chute avec le vent horizontal

Abstract

Solution stationnaire de l'e Âquation de coagulation de gouttelettes en chute avec le vent horizontal MERIEM MERAD (*)-HANANE BELHIRECHE (*)-HISAO FUJITA YASHIMA (**) ABSTRACT-We consider the equation which describes the coagulation process of water drops which fall in the air. The equation is considered in a two-dimensional domain and the density of water drops entering the domain is supposed to be given. Under the hypothesis of the constancy of the horizontal wind and some suitable conditions, we prove the existence and the uniqueness of the stationary solution. RE  SUME Â-On conside Áre l'e Âquation de Âcrivant le processus de coagulation des gouttelettes qui tombent dans l'air. L'e Âquation est conside Âre Âe dans un domaine de dimension 2 et la densite  des gouttelettes a Á l'entre Âe du domaine est suppose Âe donne Âe. Sous l'hypothe Áse que la vitesse de l'air est constante dans la direction horizontale et quelques autres conditions convenables, on prouve l'existence et l'unicite  de la solution stationnaire.

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.…”

“…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. 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.…”