# Some Properties of Blow up Solutions in the Cauchy Problem for 3D Navier–Stokes Equations

## Abstract

**:**

## 1. Introduction

## 2. Main Alternative

**Theorem**

**1.**

**Proof.**

**Lemma**

**1.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

## 3. Estimates of Kinetic Energy of the Flow

**Theorem**

**2.**

**Proof.**

## 4. Lower Bounds on the Length of the Regularity Interval

**Theorem**

**3.**

**Proof.**

**Remark**

**3.**

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Semenov, V.I.
Some Properties of Blow up Solutions in the Cauchy Problem for 3D Navier–Stokes Equations. *Symmetry* **2020**, *12*, 1523.
https://doi.org/10.3390/sym12091523

**AMA Style**

Semenov VI.
Some Properties of Blow up Solutions in the Cauchy Problem for 3D Navier–Stokes Equations. *Symmetry*. 2020; 12(9):1523.
https://doi.org/10.3390/sym12091523

**Chicago/Turabian Style**

Semenov, Vladimir I.
2020. "Some Properties of Blow up Solutions in the Cauchy Problem for 3D Navier–Stokes Equations" *Symmetry* 12, no. 9: 1523.
https://doi.org/10.3390/sym12091523