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

作者：Bae Hantaek^*; Biswas Animikh; Tadmor Eitan

来源：Archive for Rational Mechanics and Analysis, 2012, 205(3): 963-991.

DOI：10.1007/s00205-012-0532-5

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.

• 出版日期2012-9