We study the homogenization problem for the evolutionary Navier-Stokes system under the critical size of obstacles. Convergence towards the limit system of Brinkman's type is shown under very mild assumptions concerning the shape of the obstacles and their mutual distance.
We study the regularity criterion for the Navier‐Stokes equations in terms of one directional derivative of the velocity field. Using a suitable multiplicative Sobolev inequality we extend the results by Kukavica & Ziane, Cao and Zhang.
We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.
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