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Existence and Uniqueness of the Solution to the Dissipative 2D Quasi-Geostrophic Equations in the Sobolev Space

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We study the two dimensional dissipative quasi-geostrophic equations in the Sobolev space Existence and uniqueness of the solution local in time is proved in Hs when s>2(1−α). Existence and uniqueness of the solution global in time is also proved in Hs when s≥2(1−α) and the initial data is small. For the case, s>2(1−α), we also obtain the unique large global solution in Hs provided that is small enough.

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Authors and Affiliations

  1. Department of Mathematics, 401 Mathematical Sciences, Oklahoma State University, Stillwater, OK, 74078, USA

    Ning Ju

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  1. Ning Ju
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Correspondence to Ning Ju.

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Communicated by P. Constantin

Acknowledgement The author thanks Professor Jiahong Wu for useful conversations, Professor Antonio Cordoba for kindly providing their preprints and Professor Peter Constantin for kind suggestions and encouragement. This work is partially supported by the Oklahoma State University, School of Art and Science new faculty start-up fund and by the Dean’s Incentive Grant.

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Ju, N. Existence and Uniqueness of the Solution to the Dissipative 2D Quasi-Geostrophic Equations in the Sobolev Space. Commun. Math. Phys. 251, 365–376 (2004). https://doi.org/10.1007/s00220-004-1062-2

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  • DOI: https://doi.org/10.1007/s00220-004-1062-2

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