Electron. J. Differential Equations, Vol. 2021 (2021), No. 89, pp. 1-9.

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

Nguyen Anh Dao, Jesus Ildefonso Diaz

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

where w =rot u, then u is regular on (0,T]. Our conclusions improve some results by Fan et al. [5].

Submitted August 3, 2021. Published November 3, 2021.
Math Subject Classifications: 35Q35, 35B65, 76D05.
Key Words: Besov space; Navier-Stokes equations; regularity criteria.

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Nguyen Anh Dao
Institute of Applied Mathematics
University of Economics Ho Chi Minh City
Ho Chi Minh City, Viet Nam
email: anhdn@ueh.edu.vn
Jesus Ildefonso Díaz
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
28040 Madrid, Spain
email: jidiaz@ucm.es

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