Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111220
Title: Exact Solutions to the Navier–Stokes Equations with Couple Stresses
Authors: Baranovskii, E. S.
Burmasheva, N. V.
Prosviryakov, E. Yu.
Issue Date: 2021
Publisher: MDPI AG
MDPI AG
Citation: Baranovskii E. S. Exact Solutions to the Navier–Stokes Equations with Couple Stresses / E. S. Baranovskii, N. V. Burmasheva, E. Yu. Prosviryakov // Symmetry. — 2021. — Vol. 13. — Iss. 8. — 1355.
Abstract: This article discusses the possibility of using the Lin–Sidorov–Aristov class of exact solutions and its modifications to describe the flows of a fluid with microstructure (with couple stresses). The presence of couple shear stresses is a consequence of taking into account the rotational degrees of freedom for an elementary volume of a micropolar liquid. Thus, the Cauchy stress tensor is not symmetric. The article presents exact solutions for describing unidirectional (layered), shear and three-dimensional flows of a micropolar viscous incompressible fluid. New statements of boundary value problems are formulated to describe generalized classical Couette, Stokes and Poiseuille flows. These flows are created by non-uniform shear stresses and velocities. A study of isobaric shear flows of a micropolar viscous incompressible fluid is presented. Isobaric shear flows are described by an overdetermined system of nonlinear partial differential equations (system of Navier–Stokes Equations and incompressibility equation). A condition for the solvability of the overdetermined system of equations is provided. A class of nontrivial solutions of an overdetermined system of partial differential equations for describing isobaric fluid flows is constructed. The exact solutions announced in this article are described by polynomials with respect to two coordinates. The coefficients of the polynomials depend on the third coordinate and time. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords: COUPLE STRESSES
EXACT SOLUTIONS
GRADIENT FLOWS
ISOBARIC FLOWS
MICROPOLAR FLUID
NAVIER–STOKES EQUATIONS
NON-SYMMETRIC STRESS TENSOR
OVERDETERMINED SYSTEM
SOLVABILITY CONDITION
URI: http://hdl.handle.net/10995/111220
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85111922099
PURE ID: 22984420
ISSN: 2073-8994
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85111922099.pdf299,71 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.