Partial Regularity Results for the Three-dimensional Incompressible Navier-Stokes Equation
Author | : Jincheng Yang (Ph. D.) |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
ISBN-10 | : OCLC:1377538959 |
ISBN-13 | : |
Rating | : 4/5 ( Downloads) |
Download or read book Partial Regularity Results for the Three-dimensional Incompressible Navier-Stokes Equation written by Jincheng Yang (Ph. D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show a series of works of some regularity results on the incompressible Navier-Stokes equation in dimension three. Using the blow-up method, we estimate the higher regularity in the Lorentz norm for smooth solutions to the Navier-Stokes equation. In particular, we show a second derivative estimate for suitable weak solutions, which improves the currently known regularity. We construct a maximal function associated with geometric objects that we call skewed cylinders, appearing in inviscid flows like the Eulerian cylinders around the Lagrangian trajectories. We also apply the blow-up method to estimate the boundary vorticity, which enables us to achieve an unconditional control of the layer separation of Leray-Hopf solutions from a steady shear flow in a finite periodic channel