= Papkovich potentials for a strained sphere
{c}
{title2=$\boldsymbol\Phi=-5a^3\mathbf E\mathbf x/(3r^3),\quad\chi=a^5(\mathbf x\cdot\mathbf E\mathbf x)/r^5$}
With symmetric traceless strain $\mathbf E$, these harmonic potentials solve the decaying disturbance around a stationary sphere in the convention $\mathbf u=\boldsymbol\Phi-\tfrac12\nabla(\mathbf x\cdot\boldsymbol\Phi+\chi)$ and $p=-\mu\nabla\cdot\boldsymbol\Phi$. The vector potential supplies the leading <stresslet>; the scalar degree-two potential corrects no slip at finite radius. Matching the independent $\mathbf E\mathbf x$ and $(\mathbf x\cdot\mathbf E\mathbf x)\mathbf x$ structures fixes both coefficients.
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