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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
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