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Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces L p or \(\dot{H}^{-1/2}\)

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Abstract

In this paper we study the 2D quasi-geostrophic equation with and without dissipation. We give global existence results of weak solutions for an initial data in the space L p or \(\dot{H}^{-1/2}\) . In the dissipative case, when the initial data is in L p, p > 2, we give a regularity result of these solutions.

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  1. Département de Mathématiques, Université d’Evry Boulevard F. Mitterrand, 91025, Evry Cedex, France

    Fabien Marchand

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  1. Fabien Marchand
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Correspondence to Fabien Marchand.

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Communicated by P. Constantin

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Marchand, F. Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces L p or \(\dot{H}^{-1/2}\) . Commun. Math. Phys. 277, 45–67 (2008). https://doi.org/10.1007/s00220-007-0356-6

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  • DOI: https://doi.org/10.1007/s00220-007-0356-6

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