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A note on potential Type II blowups of axisymmetric solutions to the Navier-Stokes equations

Gregory Seregin

Abstract

In the note, a certain scenario of potential Type II blowups of axisymmetric solutions to the Navier-Stokes equations is considered. The main tool of the treatment of such blowups is the corresponding Euler scaling.

A note on potential Type II blowups of axisymmetric solutions to the Navier-Stokes equations

Abstract

In the note, a certain scenario of potential Type II blowups of axisymmetric solutions to the Navier-Stokes equations is considered. The main tool of the treatment of such blowups is the corresponding Euler scaling.
Paper Structure (4 sections, 7 theorems, 114 equations)

This paper contains 4 sections, 7 theorems, 114 equations.

Table of Contents

  1. Type II Blowups
  2. Axial Symmetry
  3. Self-Similarity and Axial Symmetry
  4. Discrete Self-Similarity and Axial Symmetry

Key Result

Proposition 1.1

Suppose that a pair $v$ and $q$ is a suitable weak solution to the Navier-Stokes equations in the unit space-time cylinder $Q$. Assume $v$ and $q$ satisfy the conditions m-order, growthcond, and secondderiveNsl. Then, there are two functions $u$ and $p$ defined in $Q_-=\mathbb R^3\times]-\infty,0[$, in $Q_-=\mathbb R^3\times ]-\infty,0[$ in the sense of distributions; for a.a. $\tau_0\in ]-\infty,

Theorems & Definitions (12)

  • Proposition 1.1
  • Lemma 2.1
  • proof
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Corollary 2.4
  • Proposition 3.1
  • proof
  • ...and 2 more