Author

Reinhard Farwig

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Preprint Aug 2026

The Stokes Operator on Exterior Domains in Homogeneous Weighted Function Spaces:From Weak Theory to $\mathscr H^\infty$-calculus to Fractional Domains

We consider the Stokes operator $A$ on smooth exterior domains $\Omega$ of $\mathbb{R}^n$ in homogeneous Sobolev spaces $\widehat H^{\kappa,q}_w(\Omega)$ with radially symmetric Muckenhoupt weights $w\in \mathscr A_q$. A fundamental property is the existence of a bounded $\mathscr H^\infty$-calculus of the Stokes opera...

Reinhard Farwig, Kazuyuki Tsuda · 0 citations

Preprint Aug 2026

Time periodic problem of the Navier-Stokes equations in an exterior domain with periodically moving boundary

In this paper we consider the Navier-Stokes equations in exterior domains of $\mathbb{R}^n$, $n\geq 3$, with a periodically in time moving boundary $\partial\Omega(t)$ and external force $f(t)$. For this case we prove the existence of a locally unique mild time periodic solution in weighted function spaces with radiall...

Reinhard Farwig, Kazuyuki Tsuda · 1 citation