The weak Stokes problem associated with a flow through a profile cascade in Lr-framework

2020/09/17 by Tomáš Neustupa, Neustupa, Tomáš
Computer Science · Engineering · Mathematics · #35Q30 #76D03 #76D05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2009.08234

openalex publication_date 2020/09/17 · openalex created_date 2020/09/21 · openalex updated_date 2026/07/28

Abstract

We study the weak steady Stokes problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade, in the Lr-framework. The used mathematical model is based on the reduction to one spatial period, represented by a bounded 2D domain Omega. The corresponding Stokes problem is formulated by means of three types of boundary conditions: the conditions of periodicity on the "lower" and "upper" parts of the boundary, the Dirichlet boundary conditions on the "inflow" and on the profile and an artificial "do nothing"--type boundary condition on the "outflow". Under appropriate assumptions on the given data, we prove the existence and uniqueness of a weak solution in W^1,r(Omega) and its continuous dependence on the data. We explain the sense in which the "do nothing" boundary condition on the "outflow" is satisfied.

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