Remarks on self-similar solutions for the surface quasi-geostrophic equation and its generalization

Cannone, Marco; Xue, Liutang

doi:10.1090/S0002-9939-2015-12468-9

Remarks on self-similar solutions for the surface quasi-geostrophic equation and its generalization
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by Marco Cannone and Liutang Xue

Proc. Amer. Math. Soc. 143 (2015), 2613-2622

DOI: https://doi.org/10.1090/S0002-9939-2015-12468-9

Published electronically: February 16, 2015

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Abstract:

We prove some nonexistence results of self-similar singular solutions for the surface quasi-geostrophic equation and its generalization by relying on the fundamental local $L^p$-inequality of the self-similar quantity.

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