Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces

Date

2021-11-03

Authors

Dao, Nguyen Anh
Diaz, Jesus Ildefonso

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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].

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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.

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Attribution 4.0 International

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