= Weakly compliant sphere-plane squeeze flow
{title2=$H=H_0+R^2/2+\varepsilon P$}
A sphere approaching a locally compliant elastic coating has a <parabolic lubrication gap> increased by pressure-induced downward surface displacement. With a local compliance $\eta$, the dimensionless compliance is $\varepsilon=\eta\mu a\widehat v/\widehat h^3$. The gap is $H=H_0+R^2/2+\varepsilon P$ and its <Reynolds lubrication equation> is $12H_T=R^{-1}(RH^3P_R)_R$. The rigid term is $P_0=-3\dot H_0/(H_0+R^2/2)^2$. The first elastic correction contains both $\dot H_0^2$ and $\ddot H_0$: elastic gap evolution retains the time derivative of pressure even when fluid inertia is negligible.
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