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Stability of 2D incompressible flows in ${\bf R}^3$

Piotr B. Mucha
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Abstract

We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only assumption which is required is smallness of the $L_2$-norm of initial perturbation or its derivative with respect to the `$z$'-coordinate in the same norm. The magnitude of the rest of the norm of initial datum is not restricted.

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Piotr B. Mucha. 2007-03-28. Stability of 2D incompressible flows in ${\bf R}^3$. https://arxiv.org/abs/math/0703844

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