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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 1, pp 189–197 | Cite as

Existence and Stability of Spatial Plane Waves for the Incompressible Navier–Stokes in \(\mathbb {R}^3\)

  • Simão Correia
  • Mário Figueira
Article
  • 99 Downloads

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.

Keywords

Incompressible Navier–Stokes local well-posedness stability spatial plane waves 

Mathematics Subject Classification

35B35 35Q30 76D03 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.CMAF-CIO and FCULLisboaPortugal

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