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- Bae, Hantaek
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Analyticity and Decay Estimates of the Navier-Stokes Equations in Critical Besov Spaces
- Author(s)
- Bae, Hantaek, Biswas, Animikh, Tadmor, Eitan
- Issued Date
- 2012-09
- 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
- Publisher
- SPRINGER
- ISSN
- 0003-9527
- Keyword
- WEAK SOLUTIONS, GEVREY REGULARITY, INITIAL DATA, LEVEL SETS, VORTICITY, POSEDNESS, BEHAVIOR, SCALE, 3D
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