arXiv subjects

Ezzeddine Zahrouni

Publications and source records attributed to Ezzeddine Zahrouni.

2 recordsLinked to original sources

arXiv2011

A Semi Discrete Dynamical System for a 2D Dissipative Quasi Geostrophic Equation

A semi-discretization in time, according to a full implicit Euler scheme, for a 2D dissipative quasi geostrophic equation, is studied. We prove existence, uniqueness and regularity results of the solution to the predicted discretization, in the subcritical case for any initial data in $\dot{L}^2$. Hence, we define an infinite semi-discrete dynamical system, then we prove the existence and the regularity of the corresponding global attractor, for a source term $f$ in $\dot{L}^{p_α}$, for a fixed $p_α = \frac{2}{1-α} $.

math.NA↗

arXiv2009

Global Existence of Solutions to the 2D subcritical dissipative Quasi-Geostrophic equation and persistency of the initial regularity

In this paper, we prove that if the initial data $θ_0$ and its Riesz transforms ($\mathcal{R}_1(θ_0)$ and $\mathcal{R}_2(θ_0)$) belong to the space $(\overline{S(\mathbb{R}^2))}^{B_{\infty}^{1-2α,\infty}}$, where $α\in ]1/2,1[$, then the 2D Quasi-Geostrophic equation with dissipation $α$ has a unique global in time solution $θ$. Moreover, we show that if in addition $θ_0 \in X$ for some functional space $X$ such as Lebesgue, Sobolev and Besov's spaces then the solution $θ$ belongs to the space $C([0,+\infty [,X).$

math.AP↗