Gregory Seregin

In the note, the Euler scaling is used to study a certain scenario of potential Type II blowups of solutions to the Navier-Stokes equations.

In this note, we describe a way to study local regularity of a weak solution to the Navier-Stokes equations, satisfying the simplest scale-invariant restriction, with the help of zooming and duality approach to the corresponding mild bounded ancient solution.

In the paper, a new slightly supercritical condition, providing local regularity of axially symmetric solutions to the non-stationary 3D Navier-Stokes equations, is discussed. It generalises almost all known results in the local regularity theory of weak axisymmetric solutions.

In the note, a new regularity condition for axisymmetric solutions to the non-stationary 3D Navier–Stokes equations is proven. It is slightly supercritical.

The objective of the note is to prove a regularity result for weak solutions to the Navier–Stokes equations that are locally in L ∞ ( L 3 , ∞ ) L_\infty (L^{3,\infty }) . It reads that, in a sense, the number of singular points at each time is at most finite. This note is inspired by a recent paper of H. J. Choe, J. Wolf, M. Yang.

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.