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2018 Blow-up criteria for the Navier–Stokes equations in non-endpoint critical Besov spaces
Dallas Albritton
Anal. PDE 11(6): 1415-1456 (2018). DOI: 10.2140/apde.2018.11.1415

Abstract

We obtain an improved blow-up criterion for solutions of the Navier–Stokes equations in critical Besov spaces. If a mild solution u has maximal existence time T < , then the non-endpoint critical Besov norms must become infinite at the blow-up time:

lim t T u ( , t ) p , q 1 + 3 p ( 3 ) = , 3 < p , q < .

In particular, we introduce a priori estimates for the solution based on elementary splittings of initial data in critical Besov spaces and energy methods. These estimates allow us to rescale around a potential singularity and apply backward uniqueness arguments. The proof does not use profile decomposition.

Citation

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Dallas Albritton. "Blow-up criteria for the Navier–Stokes equations in non-endpoint critical Besov spaces." Anal. PDE 11 (6) 1415 - 1456, 2018. https://doi.org/10.2140/apde.2018.11.1415

Information

Received: 20 February 2017; Revised: 3 December 2017; Accepted: 14 February 2018; Published: 2018
First available in Project Euclid: 23 May 2018

zbMATH: 06881247
MathSciNet: MR3803715
Digital Object Identifier: 10.2140/apde.2018.11.1415

Subjects:
Primary: 35Q30

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 6 • 2018
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