= Boundary integral representation of Stokes flow
{title2=$c(y)u(y)=\int J(y-x)\sigma n\,dS+\int uK(y-x)n\,dS$}
For homogeneous <Stokes flow> in a smooth bounded volume, use $J_{ij}(r)=(\delta_{ij}/|r|+r_ir_j/|r|^3)/(8\pi\mu)$ and $K_{ijk}(r)=-3r_ir_jr_k/(4\pi|r|^5)$. The <Lorentz reciprocal theorem> with a point-force <Stokeslet> gives the displayed representation, with $c=1$ inside, $0$ outside and $1/2$ on a smooth boundary. The double-layer integral at the boundary has its limiting principal-value meaning. In an exterior problem the body's outward normal is opposite to the fluid-domain normal, reversing both boundary terms; a nonzero ambient flow adds its far-boundary contribution.
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