4.6 Article

Note on Leray's criterion for Navier-Stokes singularity

Related references

Note: Only part of the references are listed.
Article Mechanics

Velocity-pressure correlation in Navier-Stokes flows and the problem of global regularity

Chuong V. Tran et al.

Summary: Incompressible fluid flows are characterized by high correlations between velocity and pressure, as well as between vorticity and pressure. This correlation plays a significant role in maintaining regularity in Navier-Stokes flows. The study suggests that as long as global pressure minimum (or minima) and velocity maximum (or maxima) are mutually exclusive, regularity is likely to persist.

JOURNAL OF FLUID MECHANICS (2021)

Article Mathematics, Applied

Improved Quantitative Regularity for the Navier-Stokes Equations in a Scale of Critical Spaces

Stan Palasek

Summary: In this study, a quantitative regularity theorem and a blowup criterion for classical solutions of the three-dimensional Navier-Stokes equations satisfying critical conditions are proven. By following Tao's strategy, improved subcritical estimates for such solutions are obtained, leading to a double logarithmic lower bound on the blowup rate.Various tools are utilized, including a solution decomposition and Carleman inequality for the heat equation, to prove quantitative backward uniqueness in cylindrical regions.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021)

Article Physics, Mathematical

Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations

Chuong V. Tran et al.

JOURNAL OF MATHEMATICAL PHYSICS (2017)