• Corpus ID: 17652304

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

@article{May2009GlobalEO,
title={Global Existence of Solutions to the 2D subcritical dissipative Quasi-Geostrophic equation and persistency of the initial regularity},
author={Ramzi May and Ezzeddine Zahrouni},
journal={arXiv: Analysis of PDEs},
year={2009}
}
• Published 3 August 2009
• Mathematics
• arXiv: Analysis of PDEs
In this paper, we prove that if the initial data $\theta_0$ and its Riesz transforms ($\mathcal{R}_1(\theta_0)$ and $\mathcal{R}_2(\theta_0)$) belong to the space $(\overline{S(\mathbb{R}^2))}^{B_{\infty}^{1-2\alpha ,\infty}}$, where $\alpha \in ]1/2,1[$, then the 2D Quasi-Geostrophic equation with dissipation $\alpha$ has a unique global in time solution $\theta$. Moreover, we show that if in addition $\theta_0 \in X$ for some functional space $X$ such as Lebesgue, Sobolev and Besov's spaces…

## References

SHOWING 1-10 OF 23 REFERENCES

### Behavior of solutions of 2D quasi-geostrophic equations

• Mathematics
• 1999
We study solutions to the 2D quasi-geostrophic (QGS) equation $$\frac{\partial \theta}{\partial t}+u\cdot\nabla\theta + \kappa (-\Delta)^{\alpha}\theta=f$$ and prove global existence and uniqueness

### On the critical dissipative quasi-geostrophic equation

• Mathematics, Physics
• 2001
The 2D quasi-geostrophic (QG) equation is a two dimensional model of the 3D incompressible Euler equations. When dissipation is included in the model, then solutions always exist if the dissipation's

### Dissipative quasi-geostrophic equations with L p data

We seek solutions of the initial value problem for the 2D dissipative quasi-geostrophic (QG) equation with L p initial data. The 2D dissipative QG equation is a two dimensional model of the 3D

### Quasi-geostrophic type equations with weak initial data

Westudytheinitialvalueproblemforthequasi-geostrophictypeequations @ @t +ur+( )=0; on R n (0;1); (x;0)=0(x) ;x 2 R n ; where (0 1) is a xed parameter and u =( u j )i s divergence free and determined

### Recent Developments in the Navier-Stokes Problem

INTRODUCTION What is this Book About? SOME RESULTS OF REAL HARMONIC ANALYSIS Real Interpolation, Lorentz Spaces, and Sobolev Embedding Besov Spaces and Littlewood-Paley Decomposition Shift-Invariant

### Littlewood-Paley Theory and the Study of Function Spaces

• Mathematics
• 1991
Calderon's formula and a decomposition of $L^2(\mathbb R^n)$ Decomposition of Lipschitz spaces Minimality of $\dot B^0,1_1$ Littlewood-Paley theory The Besov and Triebel-Lizorkin spaces The $\varphi$

### Interpolation Spaces: An Introduction

• Mathematics
• 2011
1. Some Classical Theorems.- 1.1. The Riesz-Thorin Theorem.- 1.2. Applications of the Riesz-Thorin Theorem.- 1.3. The Marcinkiewicz Theorem.- 1.4. An Application of the Marcinkiewicz Theorem.- 1.5.

### A Maximum Principle Applied to Quasi-Geostrophic Equations

• Mathematics
• 2004
We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of Lp-norms and