## Methods and Applications of Analysis

- Methods Appl. Anal.
- Volume 11, Number 4 (2004), 605-634.

### Non blow-up of the 3D Euler equations for a class of three-dimensional initial data in cylindrical domains

C. Bardos, F. Golse, A. Mahalov, and B. Nicolaenko

#### Abstract

Non blow-up of the 3D incompressible Euler Equations is proven for a class of three- dimensional initial data characterized by uniformly large vorticity in bounded cylindrical domains. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to some 2D manifold. The approach of proving regularity is based on investigation of fast singular oscillating limits and nonlinear averaging methods in the context of almost periodic functions. We establish the global regularity of the 3D limit resonant Euler equations without any restriction on the size of 3D initial data. After establishing strong convergence to the limit resonant equations, we bootstrap this into the regularity on arbitrary large time intervals of the solutions of 3D Euler Equations with weakly aligned uniformly large vorticity at $t = 0$.

#### Article information

**Source**

Methods Appl. Anal., Volume 11, Number 4 (2004), 605-634.

**Dates**

First available in Project Euclid: 13 April 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.maa/1144939949

**Mathematical Reviews number (MathSciNet)**

MR2195372

**Zentralblatt MATH identifier**

1103.35083

**Subjects**

Primary: 35Q35: PDEs in connection with fluid mechanics

Secondary: 35B35: Stability 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]

#### Citation

Mahalov, A.; Nicolaenko, B.; Bardos, C.; Golse, F. Non blow-up of the 3D Euler equations for a class of three-dimensional initial data in cylindrical domains. Methods Appl. Anal. 11 (2004), no. 4, 605--634. https://projecteuclid.org/euclid.maa/1144939949