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Électromagnétisme  Electromagnetism  Modèles mathématiques  Mathematical models
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Differential equations, Partial  Electromagnetic theory  Integrodifferential equations  Mechanics  519.6  681.3*G19  681.3*G19 Integral equations: Fredholm equations; integrodifferential equations; Volterra equations (Numerical analysis)  Integral equations: Fredholm equations; integrodifferential equations; Volterra equations (Numerical analysis)  519.6 Computational mathematics. Numerical analysis. Computer programming  Computational mathematics. Numerical analysis. Computer programming  Light, Electromagnetic theory of  Electric fields  Magnetic fields  Classical mechanics  Newtonian mechanics  Physics  Dynamics  Quantum theory  Improperly posed problems in integrodifferential equations  Improperly posed problems in partial differential equations  Improperly posed problems  Illposed problems  Differential equations  Mathematical physics  Classical mechanics. Field theory  Electromagnetism. Ferromagnetism
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The theory of incompressible multipolar viscous fluids is a nonNewtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The NavierStokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard NavierStokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most nonNewtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higherorder boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the NavierStokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
NonNewtonian fluids.  Fluid dynamics.  Mathematics.  Partial differential equations.  Mathematical physics.  Fluids.  Mathematical Physics.  Partial Differential Equations.  Fluid and Aerodynamics.  Dynamics  Fluid mechanics  Newtonian fluids  Rheology  Viscous flow  Differential equations, partial.  Partial differential equations  Hydraulics  Mechanics  Physics  Hydrostatics  Permeability  Physical mathematics  Mathematics
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Plates (Engineering)  Buckling (Mechanics)  Plaques (Ingénierie)  Flambage (Résistance des matériaux)  Buckling (Mechanics).  Plates (Engineering).  Bouwmechanica  Stabiliteit  Sterkteleer  Disks (Mechanics)  Panels  Structural plates  Elastic plates and shells  Structural analysis (Engineering)  Shells (Engineering)  Deformations (Mechanics)  Plasticity  Strains and stresses  Structural failures
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Mathematics  Partial differential equations  Differential equations  Mathematical physics  Fluid mechanics  vloeistofstroming  differentiaalvergelijkingen  thermodynamica  aerodynamica  wiskunde  wiskunde  fysica
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