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arXiv · 0910.0998

Global well-posedness for a Modified 2D dissipative quasi-geostrophic equation with initial data in the critical Sobolev space $H^1$

Ramzi May
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Abstract

In this paper, we consider the following modified quasi-geostrophic equations $\partial_tθ+Λ^αθ+u\vec\nablaθ=0$, $u=Λ^{α-1}\mathcal{R}^\perp(θ)$ where $α\in ]0,1[$ is a fixed parameter. This equation was recently introduced by P. Constantin, G. Iyer and J. Wu in \cite{CIW} as a modification of the classical quasi-geostrophic equation. In this paper, we prove that for any initial data $θ_\ast$ in the Sobolev space $H^1(\mathbb{R}^2),$ the equation (MQG) has a global and smooth solution $θ$ in $C(\mathbb{R}^{+},H^1(\mathbb{R}^2)) .$

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Ramzi May. 2009-10-06. Global well-posedness for a Modified 2D dissipative quasi-geostrophic equation with initial data in the critical Sobolev space $H^1$. https://arxiv.org/abs/0910.0998

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