Localization of spectrum bottom for the Stokes operator in a random porous medium.(English. Russian original)Zbl 0970.35102

Sib. Math. J. 42, No. 2, 386-413 (2001); translation from Sib. Mat. Zh. 42, No. 2, 451-483 (2001).
The article is devoted to the spectral theory for the Stokes operator in a random porous medium. The author exposes a series of theorems which assert that the principal eigenvalue of the Stokes system $\Delta U - \nabla p + f = 0,\quad \nabla\cdot U = 0$ on a random subdomain of a cube with edge $$r$$ has the order $$O(\ln^{-2/d}r)$$ with probability arbitrarily close to unity. A determinate interval is also indicated which contains this random variable with probability arbitrarily close to unity.

MSC:

 35Q30 Navier-Stokes equations 35P15 Estimates of eigenvalues in context of PDEs 60H30 Applications of stochastic analysis (to PDEs, etc.)
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