Browsing by Subject "Navier-Stokes equation"

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    Partial regularity results for the three-dimensional incompressible Navier-Stokes equation
    (2022-04-01) Yang, Jincheng, Ph. D.; Caffarelli, Luis A.; Vasseur, Alexis F.; Vicol, Vlad C; Vishik, Mikhail M
    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.