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arXiv · 1406.0693

Stability of two-dimensional Navier-Stokes motions in the periodic case

Wojciech Zajączkowski·Ewa Zadrzyńska
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Abstract

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong three-dimensional solutions under the assumption that the initial data and the external force are sufficiently close to the initial data and the external force of the two-dimensional problem in appropriate spaces. The second result can be treated as stability of strong two-dimensional solutions in the set of suitably strong three-dimensional motions.

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Wojciech Zajączkowski, Ewa Zadrzyńska. 2014-06-03. Stability of two-dimensional Navier-Stokes motions in the periodic case. https://arxiv.org/abs/1406.0693

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