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dc.contributor.authorBessaih, Hakima
dc.contributor.authorMaris, Razvan Florian
dc.date.accessioned2017-01-02T09:28:29Z
dc.date.available2017-01-02T09:28:29Z
dc.date.issued2015-11-02
dc.identifier.citationBessaih H, Maris F (2015) Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition. Applicable Analysis 95: 2703–2735. Available: http://dx.doi.org/10.1080/00036811.2015.1107546.
dc.identifier.issn0003-6811
dc.identifier.issn1563-504X
dc.identifier.doi10.1080/00036811.2015.1107546
dc.identifier.urihttp://hdl.handle.net/10754/622413
dc.description.abstractThe two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
dc.description.sponsorshipHakima Bessaih was partially supported by NSF [grant number DMS-1418838].
dc.publisherInforma UK Limited
dc.subjectboundary noise
dc.subjectHomogenization
dc.subjectNavier–Stokes equations
dc.subjectPerforated medium
dc.subjectSlip boundary condition
dc.titleHomogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.identifier.journalApplicable Analysis
dc.contributor.institutionDepartment of Mathematics, University of Wyoming, Laramie, WY, United States
dc.identifier.arxivid1411.6303
kaust.personMaris, Razvan Florian
dc.date.published-online2015-11-02
dc.date.published-print2016-12


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