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arXiv · 1611.10232

Existence and stability of spatial plane waves for the incompressible Navier-Stokes in $\mathbb{R}^3$

Simão Correia·Mário Figueira
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Abstract

We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a $L^\infty$ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes $L^3(\mathbb{R}^3)$ and these solutions. Finally, we prove $L^3$-stability of spatial plane waves, with no condition on their size.

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Simão Correia, Mário Figueira. 2016-11-30. Existence and stability of spatial plane waves for the incompressible Navier-Stokes in $\mathbb{R}^3$. https://doi.org/10.1007/s00021-017-0317-6

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