Liouville theorems for the Stokes equations with applications to large time estimates

Ken Abe

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arXiv · 1807.04436

Liouville theorems for the Stokes equations with applications to large time estimates

Ken Abe

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Abstract

We study Liouville theorems for the non-stationary Stokes equations in exterior domains in $ \mathbb{R}^{n}$ under decay conditions for spatial variables. As applications, we prove that the Stokes semigroup is a bounded analytic semigroup on $L^{ \infty}_{ \sigma}$ of angle $ \pi/2$ for $n \geq 3$. We also prove large time estimates for $n=2$ with zero net force.

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Ken Abe. 2018-07-12. Liouville theorems for the Stokes equations with applications to large time estimates. https://arxiv.org/abs/1807.04436

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