• Corpus ID: 245906197

# Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces

@inproceedings{Feng2022QuantitativeBF,
title={Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces},
author={Wenquan Feng and Jiao He and Weinan Wang},
year={2022}
}
• Published 12 January 2022
• Mathematics
In this paper, we prove a quantitative regularity theorem and blow-up criterion of classical solutions for the three-dimensional Navier-Stokes equations. By adapting the strategy developed by Tao in [20], we obtain an explicit blow-up rate in the setting of critical Lorentz spaces L0 (R) with 3 ≤ q0 < ∞. Our results improve the previous regularity in critical Lebesgue spaces L(R) in [20] and quantify the qualitative result by Phuc in [16].
7 Citations
• Mathematics
• 2022
. We are concerned with strong axisymmetric solutions to the 3D incompressible Navier-Stokes equations. We show that if the weak L 3 norm of a strong solution u on time interval [0 , T ] is bounded
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For any divergence free initial datum u0 with ‖u0‖∞ + ‖∇u0‖Lp + ‖∇u0‖Lp < ∞ for some p > d (d ≥ 2), the well-posedness and smoothness are proved for incompressible Navier-Stokes equations on R or T
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By proposing and solving future distribution dependent SDEs, the well-posedness and regularity are derived for (generalized) incompressible Navier-Stokes equations on R or T := R/Z (d ≥ 1). AMS
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By proposing and solving future distribution dependent SDEs, the well-posedness and regularity are derived for (generalized) incompressible Navier-Stokes equations on R or T := R/Z (d ≥ 1) for given

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