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The Stokes equations in exterior $$n$$-dimensional domains. (English) Zbl 1166.76015
Summary: The aim is the construction and representation of solutions $$u,p$$ to homogeneous Stokes equations
$-\Delta u+\nabla p=0 \quad\text{in }G_e, \qquad \nabla\cdot u=0 \quad\text{in }G_e, \qquad u=\Phi \quad\text{on }\Gamma,$
with methods of hydrodynamical potential theory. Here $$G_e\subset\mathbb R^n$$ $$(n\geq 2)$$ is an exterior domain with boundary $$\Gamma=\partial G_e\in C^2$$, and $$\Phi\in C^0(\Gamma)$$ is some prescribed boundary value.
##### MSC:
 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D07 Stokes and related (Oseen, etc.) flows 35Q30 Navier-Stokes equations