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General Nonlocal Model Describing the Laminar and Turbulent Flows of Viscous and Nonlinear Viscous Fluids and Its Investigation
Author(s) -
Litvinov William G.
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200012)220:1<79::aid-mana79>3.0.co;2-3
Subject(s) - laminar flow , turbulence , mathematics , nonlinear system , viscous liquid , mechanics , reynolds number , viscosity , navier–stokes equations , flow (mathematics) , herschel–bulkley fluid , classical mechanics , mathematical analysis , physics , compressibility , geometry , thermodynamics , quantum mechanics
A general nonlocal model describing the flows of viscous and nonlinear viscous fluids for both laminar and turbulent flows is introduced and studied. For this model, the viscosity of the fluid depends on the second invariant of the rate of the strain tensor and on a nonlocal (integral) characteristic of the flow. This characteristic is a vector that, in the simplest case, is an analog of the Reynolds number. For slow flows, the model turns into the Navier–Stokes equations or into the equations of a nonlinear viscous fluid. Problems on steady and nonsteady flows with mixed boundary conditions when velocities and surface forces are prescribed on different parts of the boundary are studied. Existence results without restrictions on the smallness of data and on the length of the interval of time are proved.