On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary

نویسندگان

چکیده

Long-time and large-data existence of weak solutions for initial- boundary-value problems concerning three-dimensional flows \emph{incompressible} fluids is nowadays available not only Navier--Stokes but also various fluid models where the relation between Cauchy stress tensor symmetric part velocity gradient \emph{nonlinear}. The majority such studies however concerns a dependence \emph{explicit} (the function gradient), which makes class studied unduly restrictive. same boundary conditions, or more precisely slipping mechanisms on boundary, no-slip still most preferred condition considered in literature. Our main objective to develop robust mathematical theory unsteady internal \emph{implicitly constituted} incompressible with implicit relations tangential projections normal traction boundary. covers numerous rheological used chemistry, biorheology, polymer food industry as well geomechanics. It includes, special cases, nonlinear slip stick-slip conditions. Unlike earlier studies, conditions characterizing admissible classes constitutive equations are expressed by means tools elementary calculus. In addition, fully constructive proof (approximation scheme) incorporated. Finally, we focus question uniqueness solutions.

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ژورنال

عنوان ژورنال: Journal of Mathematical Fluid Mechanics

سال: 2023

ISSN: ['1422-6952', '1422-6928']

DOI: https://doi.org/10.1007/s00021-023-00803-w