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arXiv · 1912.01193

On the large time $L^{\infty}$-estimates of the Stokes semigroup in two-dimensional exterior domains

Ken Abe
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Abstract

We prove that the Stokes semigroup is a bounded analytic semigroup on $L^{\infty}_{\sigma}$ of angle $\pi/2$ for two-dimensional exterior domains. This result is an end point case of the $L^{p}$-boundedness of the semigroup for $p\in (1,\infty)$, established by Borchers and Varnhorn (1993) and an extension of finite time $L^{\infty}$-estimates studied by the author and Giga (2014). The proof is based on the non-existence result of bounded steady flows (the Stokes paradox) and some asymptotic formula for the net force of the Stokes resolvent.

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Ken Abe. 2019-12-03. On the large time $L^{\infty}$-estimates of the Stokes semigroup in two-dimensional exterior domains. https://arxiv.org/abs/1912.01193

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