Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces
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Date
2021-11-03
Authors
Dao, Nguyen Anh
Diaz, Jesus Ildefonso
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We investigate a logarithmically improved regularity criteria in terms of the velocity, or the vorticity, for the Navier-Stokes equations in homogeneous Besov spaces. More precisely, we prove that if the weak solution u satisfies either
∫T0 ∥u(t)∥2/1-αḂ-α∞,∞ /1 + log+ ∥u(t)∥H˙s0dt < ∞,
or ∫T0 ∥w(t)∥2/2-αḂ-α∞,∞ /1 + log+ ∥w(t)∥H˙s0 dt < ∞,
where w = rot u, then u is regular on (0, T]. Our conclusions improve some results by Fan et al. [5].
Description
Keywords
Besov space, Navier-Stokes equations, Regularity criteria
Citation
Dao, N. A., & Díaz, J. I. (2021). Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces. <i>Electronic Journal of Differential Equations, 2021</i>(89), pp. 1-9.