# 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} }

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

### Quantitative control of solutions to axisymmetric Navier-Stokes equations in terms of the weak $L^3$ norm

- 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…

### Well-posedness, Smoothness and Blow-up for Incompressible Navier-Stokes Equations

- Mathematics
- 2022

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…

### A P ] 2 4 Ja n 20 22 Existence , Uniqueness and Smoothness for Incompressible Navier-Stokes Equations

- Mathematics, Philosophy
- 2022

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…

### Localized quantitative estimates and potential blow-up rates for the Navier-Stokes equations

- Mathematics
- 2022

A BSTRACT . We show that if v is a smooth suitable weak solution to the Navier-Stokes equations on B (0 , 4) × (0 , T ∗ ) , that possesses a singular point ( x 0 , T ∗ ) ∈ B (0 , 4) ×{ T ∗ } , then…

### Well-Posedness and Regularity for Navier-Stokes Equations

- Philosophy
- 2022

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…

### Existence, Uniqueness and Smoothness for Incompressible Navier-Stokes Equations ∗

- Mathematics
- 2022

For any divergence free initial datum u 0 with (cid:107) u 0 (cid:107) ∞ + (cid:107)∇ u 0 (cid:107) L p + (cid:107)∇ 2 u 0 (cid:107) L p < ∞ for some p > d ( d ≥ 2), the well-posedness and smoothness…

### A Probabilistic Characterization on Navier-Stokes Equations ∗

- Philosophy
- 2022

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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