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Rescalings at possible singularities of Navier-Stokes equations in half-space


Authors: G. Seregin and V. Šverák
Original publication: Algebra i Analiz, tom 25 (2013), nomer 5.
Journal: St. Petersburg Math. J. 25 (2014), 815-833
MSC (2010): Primary 35Q30, 76D05
DOI: https://doi.org/10.1090/S1061-0022-2014-01317-9
Published electronically: July 18, 2014
MathSciNet review: 3184609
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Abstract: The relationship is clarified between a possible blow-up for strong solutions of the initial boundary value problem for the incompressible Navier-Stokes equations in $ \{x_3>0\}$, and the Liouville theorem for mild bounded ancient solutions.


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Additional Information

G. Seregin
Affiliation: Oxford University, United Kingdom; St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: seregin@pdmi.ras.ru

V. Šverák
Affiliation: University of Minnesota
Email: sverak@math.umn.edu

DOI: https://doi.org/10.1090/S1061-0022-2014-01317-9
Keywords: Incompressible Navier--Stokes equations, blow-up, mild bounded ancient solution
Received by editor(s): January 7, 2013
Published electronically: July 18, 2014
Article copyright: © Copyright 2014 American Mathematical Society