الحل العام لمعادلة شبه المغناطيسية في بعدين في فضاء بزوف الدالي

Abstract

The main goal of this thesis is to study the two-dimensional quasi-geostrophic equation. This equation serves as two-dimensional models arising in geophysical fluid dynamics. We aim to study the global and local existence and uniqueness result for quasi-geostrophic equation with initial data ,that is we are interested to study the following system.

{█(∂_t θ +v∙∇θ + |D|^(1/2) θ =0 , (x,t)∈R^2×[0,∞┤[@div v=0,@├ θ┤|_(t=0)=θ_0.)┤

The problem is solved in many functional spaces, with small initial data. We will study the paper [15] and apply these results to our case. More precisely, we will prove the problem for θ_0∈B_2,1^s, with s>3/2, where B_2,1^s is the Besov space given in Chapter II. Finally,