Finite element approximation of steady flows of generalized Newtonian fluids with concentration-dependent power-law index

Ko, Seungchan; Süli, Endre

doi:10.48550/arxiv.1708.07830

Cited by 1 publication

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“…From the viewpoint of computational mathematics, in [14], a construction of a conforming finite element approximation of the stationary model was considered and the convergence analysis of the numerical method was developed in the case of variable-exponent spaces in a two dimensional domain. Subsequently, the analysis was extended to three space dimensions in [15] by using a slightly different numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

Existence of global weak solutions for unsteady motions of incompressible chemically reacting generalized Newtonian fluids

Ko¹

2018

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We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations with a power-law type stress-strain relation, where the power-law index depends on the concentration of a chemical, coupled to a convection-diffusion equation for the concentration. This system of equations arises in the rheology of the synovial fluid found in the cavities of synovial joints. We prove the existence of global weak solutions of the non-stationary model by using the Galerkin method combined with generalized monotone operator theory and parabolic De Giorgi-Nash-Moser theory. As the governing equations involve a nonlinearity with a variable power-law index, our proofs exploit the framework of generalized Sobolev spaces with variable integrability exponent.

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Section: Introductionmentioning

confidence: 99%