By Frédéric Alliot, Cherif Amrouche (auth.), Adélia Sequeira, Hugo Beirão da Veiga, Juha Hans Videman (eds.)
This ebook is intended as a gift to honor Professor at the th get together of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from 11 international locations. They disguise many alternative components of analysis on the topic of the paintings of Professor together with Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of ideas of parabolic and elliptic difficulties, operator thought and numerical equipment. the conclusion of this ebook couldn't were made attainable with no the beneficiant aid of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. specific thank you are as a result of Dr. Ulrych for the cautious guidance of the ultimate model of this booklet. final yet now not least, we want to show our gratitude to Dr. for her valuable the help of the very starting. This venture couldn't were effectively concluded with no her enthusiasm and loving take care of her father. On behalf of the editors ADÉLIA SEQUEIRA v commemorated by means of the Order of benefit of the Czech Republic via Václav Havel, President of the Czech Republic, at the October 28, 1998, Professor Emeritus of arithmetic on the Charles collage in Prague, Presidential learn Professor on the Northern Illinois college and health professional Honoris Causa on the Technical collage of Dresden, has been enriching the Czech and international arithmetic along with his new rules within the parts of partial differential equations, nonlinear sensible research and purposes of the either disciplines in continuum mechanics and hydrodynamics for greater than 40 years.
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J. , 41:363– 386. Proudman, I. H. (1954). On the decay of a normally distributed and homogeneous turbulent velocity field. Philos. Trans. Roy. Soc. London Ser. , A267:163–189. Rodi, W. (1980). Turbulence Models and Their Application in Hydraulics – A State of the Art Review. International Association for Hydraulic Research, Delft, the Netherlands.  Schumann, U. (1977). Realizability of Reynolds stress turbulence models. Phys. Fluids, 20:721–725. 32 Chen G. , Rajagopal K. , Tao L. I. (1972).
Other issues are also to be discussed such as the consequences of the symmetries of the Navier-Stokes equations, realizability and molecular dissipation. A note on turbulence modeling 21 Our main concern at this moment is the basis for the formulation. A great deal of effort has to be expended yet to construct concrete models to solve problems. 2. FORMULATION Suppose that the Navier-Stokes equations can describe the turbulent motion of incompressible Newtonian fluids in a flow domain (here it is tacitly assumed whether a physical fluid is a Newtonian fluid or not is determined by its behavior in laminar states), that is, the velocity u and the pressure are determined by, together with proper initial and boundary conditions, where and are, respectively, the mass density and the kinetic viscosity of the fluid.
26), the closed model being dissipative. 32). Though it bypasses solving the equations as well as prescribing the initial and boundary conditions, this procedure does not necessarily guarantee a proper model for due to the approximate nature of the model; for instance, depends on then and the closed set of equations may not yield solutions for compatible with that directly obtained for To remedy this flaw, we may propose a form for according to the criterion for producing reasonable solutions for from the closed model, instead of focusing on the matching of This scheme can be used even if is not available.
Applied Nonlinear Analysis by Frédéric Alliot, Cherif Amrouche (auth.), Adélia Sequeira, Hugo Beirão da Veiga, Juha Hans Videman (eds.)