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Gregory Seregin

Publications and source records attributed to Gregory Seregin.

At least 19 recordsLinked to original sources
arXiv2026

On potential Type II blowups for the Navier-Stokes equations

In the present note, certain scenarios of potential Type II blowups of solutions to the Navier-Stokes equations are considered on the local level. They generalise particular scenarios described in the previous papers of the author. The main features of the approach, adopted in the note, are a zoom based on the Euler scaling and Liouville type theorems for the Euler equations in classes motived by a particular scenario of the Type II blowup.

math.AP↗
arXiv2026

A note on certain scenarios of Type II blowups of suitable weak solutions to the Navier-Stokes equations

In the note, various scenarios of potential Type II blowups of suitable weak solutions to the Navier-Stokes equations are studied. It is shown, that under some assumptions, such type of blowups cannot happen. In this case, corresponding statements may be interpreted as regularity results. Their justification is based on a technique making use of a certain Euler scaling and Liouville type theorems for ancient solutions to the Euler system.

math.AP↗
arXiv2021

On regularity properties of a surface growth model

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.

math.AP↗
arXiv2020

Regularity of Solutions to the Navier-Stokes equations in $\dot{B}_{\infty,\infty}^{-1}$

We prove that if $u$ is a suitable weak solution to the three dimensional Navier-Stokes equations from the space $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, then all scaled energy quantities of $u$ are bounded. As a consequence, it is shown that any axially symmetric suitable weak solution $u$, belonging to $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, is smooth.

math.AP↗
arXiv2019

On Type I Blowups of Suitable Weak Solutions to Navier-Stokes Equations near Boundary

In this note, boundary Type I blowups of suitable weak solutions to the Navier-Stokes equations are discussed. In particular, it has been shown that, under certain assumptions, the existence of non-trivial mild bounded ancient solutions in half space leads to the existence of suitable weak solutions with Type I blowup on the boundary.

math.AP↗
arXiv2018

Axisymmetric flows in the exterior of a cylinder

We study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $Π=\{x=(x_{h}, x_3)\ |\ |x_{h} |>1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^{3}\cap L^{2}(Π)$ satisfying the decay condition of the swirl component $ru^θ_{0}\in L^{\infty}(Π)$.

math.AP↗