On regularity of solutions of 3D navier-stokes equations

Abstract

We consider fluid in a rotating frame under periodic boundary conditions. In our previous work we show that for typical aspect ratios of periods the solutions are regular if the rotation is fast enough and the initial data and forcing terms are very smooth. Here we use a kind of closing argument to extend the results by continuity to less smooth data. The required smoothness of the data follows from natural requirement of continuous dependence of solutions of the equations on the data in appropriate spaces.

Keywords:

• Rotating frame
• Coriolis force
• Fourier series
• resonances
• variation-of-constants formula

Additional information

Notes on contributors

J. Avrinl

1

A. Babinl

1

A. Mahalov

2

B. Nicolaenko

2