The formula is from the first paragraph in the paper "Second Kind Integral Equation Formulation of Stokes' Flows Past a Particle of Arbitrary Shape" by Power and Miranda:
... the governing equations for the auxiliary perturbed fluid velocity $\vec{v}=(v_1,v_2,v_3)$ and pressure $p$ can be approximated by the creeping motion and continuity equations $ \begin{align} &\frac{\partial^2 v_i}{\partial x_j\partial x_j}(x)=\frac{\partial p}{\partial x_i}(x)\\ &\frac{\partial v_i}{\partial x_i}(x)=0 \end{align} $
Here are my questions:
How should I understand the first formula? Is the Einstein summation convention applied here, i.e., $ \sum_j\frac{\partial^2 v_i}{\partial x_j\partial x_j}(x)=\frac{\partial p}{\partial x_i}(x)? $
Is there any reference for the derivation of the first formula? (I don't find any in the paper.)