Journal
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
Volume -, Issue -, Pages -Publisher
TEXAS STATE UNIV
Keywords
Besov space; Navier-Stokes equations; regularity criteria
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Funding
- DGISPI, Spain [MTM2017-85449-P, PID2020-112517GB-I00]
- Research Group MOMAT of the UCM [910480]
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Investigated a logarithmically improved regularity criteria for the Navier-Stokes equations in terms of the velocity or vorticity, proving that weak solutions satisfying specific integral conditions are regular for a certain time interval. This conclusion enhances some results previously obtained by Fan et al.
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 integral(T)(0) parallel to u(t)parallel to(2/1-alpha)((B)over dot infinity,infinity-alpha)/1 + log(+) parallel to u(t)parallel to((H)over dots0) dt < infinity, or integral(T)(0) parallel to w(t)parallel to(2/2-alpha)((B)over dot infinity,infinity-alpha)/1 + log(+) parallel to w(t)parallel to((H)over dots0) dt < infinity, 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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