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Remarks on a fractional diffusion transport equation with applications to the dissipative quasi-geostrophic equation

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      Abstract

      In this article I study H\"older regularity for solutions of a transport equation based in the dissipative quasi-geostrophic equation. Following a recent idea of A. Kiselev and F. Nazarov, I will use the molecular characterization of local Hardy spaces in order to obtain information on H\"older regularity of such solutions. This will be done by following the evolution of molecules in a backward equation.

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      Global well-posedness for the critical 2D dissipative quasi-geostrophic equation

      We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.
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        A local version of real Hardy spaces

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          Regularity of H\"older continuous solutions of the supercritical quasi-geostrophic equation

          We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (\(\alpha 1-2\alpha\) on the time interval \([t_0, t]\), then it is actually a classical solution on \((t_0,t]\).
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            Author and article information

            Journal
            2010-07-22
            2013-01-22
            1007.3919

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            27 pages
            math.AP
            ccsd

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