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arXiv · 1307.7837

Asymptotics of solutions to the Navier-Stokes system in exterior domains

Dragos Iftimie·Grzegorz Karch·Christophe Lacave
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Abstract

We consider the incompressible Navier-Stokes equations with the Dirichlet boundary condition in an exterior domain of $\mathbb{R}^n$ with $n\geq2$. We compare the long-time behaviour of solutions to this initial-boundary value problem with the long-time behaviour of solutions of the analogous Cauchy problem in the whole space $\mathbb{R}^n$. We find that the long-time asymptotics of solutions to both problems coincide either in the case of small initial data in the weak $L^{n}$-space or for a certain class of large initial data.

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Dragos Iftimie, Grzegorz Karch, Christophe Lacave. 2013-07-30. Asymptotics of solutions to the Navier-Stokes system in exterior domains. https://doi.org/10.1112/jlms%2Fjdu052

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