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This article is dedicated to localization of the principal eigenvalue (PE) ofthe Stokes operator acting on solenoidal vector fields that vanish outside alarge random domain modeling the pore space in a cubic block of porous materialwith disordered micro-structure. Its main result is an asymptoticallydeterministic lower bound for the PE of the sum of a low compressibilityapproximation to the Stokes operator and a small scaled random potential term,which is applied to produce a similar bound for the Stokes PE. The argumentsare based on the method proposed by F. Merkl and M. V. W\"{u}trich forlocalization of the PE of the Schr\"{o}dinger operator in a similar setting.Some additional work is needed to circumvent the complications arising from therestriction to divergence-free vector fields of the class of test functions inthe variational characterization of the Stokes PE.

A lower bound for the principal eigenvalue of the Stokes operator in a random domain