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Regularity Criterion and Energy Conservation for the Supercritical Quasi-geostrophic Equation

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Abstract

This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a new regularity condition which is weaker than all the Prodi–Serrin type regularity conditions. Moreover, we prove that any viscosity solution of the supercritical SQG in \(L^2(0,T; B^{1/2}_{2,c(\mathbb N)})\) satisfies energy equality.

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  1. Department of Mathematics, University of Illinois at Chicago, Chicago, IL,  60607, USA

    Mimi Dai

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  1. Mimi Dai
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Correspondence to Mimi Dai.

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Communicated by S. Friedlander

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Dai, M. Regularity Criterion and Energy Conservation for the Supercritical Quasi-geostrophic Equation. J. Math. Fluid Mech. 19, 191–202 (2017). https://doi.org/10.1007/s00021-017-0320-y

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  • DOI: https://doi.org/10.1007/s00021-017-0320-y

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