The Tensor of Hydrodynamic Interaction

To determine the perturbation of fluid velocity under the influence of volume forces cr, we shall begin with the equations of motion of a viscous liquid at low Reynolds numbers (Landau and Lifshitz 1987a) 

Henceforth, it is convenient to use the Fourier transforms of the velocity, pressure and volume force, correspondingly 

It is easy to see that the solution of the last set of equations takes the form 

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