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Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data

Published online by Cambridge University Press:  19 July 2013

Marius Paicu  and
Zhifei Zhang
Marius Paicu
Affiliation:
Université Bordeaux 1 Institut de Mathématiques de Bordeaux F-33405 Talence Cedex, France (marius.paicu@math.u-bordeaux1.fr)
Zhifei Zhang
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, 100871, PR China (zfzhang@math.pku.edu.cn)
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Abstract

We study the global well-posedness of 3D Navier–Stokes equations for a class of large initial data. This type of data slowly varies in the vertical direction (expressed as a function of $\varepsilon {x}_{3} $), and it is ill-prepared in the sense that its norm in ${C}^{- 1} $ will blow up at the rate ${\varepsilon }^{- \alpha } $ for $\frac{1}{2} \lt \alpha \lt 1$ as $\varepsilon $ tends to zero.

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 13 , Issue 2 , April 2014 , pp. 395 - 411
Copyright
©Cambridge University Press 2013 

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