Small-scale creation for solutions of the SQG equation

Siming He; Alexander Kiselev

doi:10.1215/00127094-2020-0064

Abstract

We construct examples of solutions to the conservative surface quasigeostrophic (SQG) equation that must either exhibit infinite-in-time growth of derivatives or blow up in finite time.

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Siming He. Alexander Kiselev. "Small-scale creation for solutions of the SQG equation." Duke Math. J. 170 (5) 1027 - 1041, 1 April 2021. https://doi.org/10.1215/00127094-2020-0064

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Received: 10 April 2019; Revised: 30 January 2020; Published: 1 April 2021

First available in Project Euclid: 18 March 2021

Digital Object Identifier: 10.1215/00127094-2020-0064

Subjects:

Primary: 35Q35

Secondary: 76B03

Keywords: 2-dimensional incompressible flow , derivatives growth , exponential growth , hyperbolic flow , small-scale creation , SQG equation

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