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Bae, Hantaek
School of Natural Science
Research Interests
  • Fluid dynamics, polymeric fluid, kinetic theory

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Analyticity and Decay Estimates of the Navier-Stokes Equations in Critical Besov Spaces

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Title
Analyticity and Decay Estimates of the Navier-Stokes Equations in Critical Besov Spaces
Author
Bae, HantaekBiswas, AnimikhTadmor, Eitan
Issue Date
2012-09
Publisher
SPRINGER
Citation
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.205, no.3, pp.963 - 991
Abstract
In this paper, we establish analyticity of the Navier-Stokes equations with small data in critical Besov spaces . The main method is Gevrey estimates, the choice of which is motivated by the work of Foias and Temam (Contemp Math 208:151-180, 1997). We show that mild solutions are Gevrey regular, that is, the energy bound holds in , globally in time for p < a. We extend these results for the intricate limiting case p = a in a suitably designed E (a) space. As a consequence of analyticity, we obtain decay estimates of weak solutions in Besov spaces. Finally, we provide a regularity criterion in Besov spaces
URI
https://scholarworks.unist.ac.kr/handle/201301/16610
URL
http://link.springer.com/article/10.1007%2Fs00205-012-0532-5
DOI
10.1007/s00205-012-0532-5
ISSN
0003-9527
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