On the role of $L^3$ and $H^{\frac{1}{2}}$ norms in hydrodynamics

Laurent Schoeffel

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arXiv · 1412.6770

On the role of $L^3$ and $H^{\frac{1}{2}}$ norms in hydrodynamics

Laurent Schoeffel

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Abstract

In this paper, we extend some results proved in previous references for three-dimensional Navier-Stokes equations. We show that when the norm of the velocity field is small enough in $L^3({I\!\!R}^3)$, then a global smooth solution of the Navier-Stokes equations is ensured. We show that a similar result holds when the norm of the velocity field is small enough in $H^{\frac{1}{2}}({I\!\!R}^3)$. The scale invariance of these two norms is discussed.

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Laurent Schoeffel. 2014-12-21. On the role of $L^3$ and $H^{\frac{1}{2}}$ norms in hydrodynamics. https://arxiv.org/abs/1412.6770

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