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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Temam Published Mathematics. The Steady-State Stokes Equations.
The Navier—Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure , temperature and density. The difference between them and the closely related Euler equations is that Navier—Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier—Stokes are a parabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure e. The Navier—Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents , water flow in a pipe and air flow around a wing.
Jan W. Fund Project: J. Following the geometric theory of abstract parabolic problems we give the detailed analysis concerning existence, uniqueness, regularization and continuation properties of the solution. For the original Navier-Stokes problem we construct next global solution of the Leray-Hopf type satisfying also Duhamel's integral formula. Focusing finally on the 3-D model with zero external force we estimate a time after which the latter solution regularizes to strong solution.
The Navier-Stokes equations describe the motion of the usual fluids like water, air, oil under quite general conditions. They are the base of the mathematical models of important phenomena in many areas of science and technology. While the physical model leading to the Navier-Stokes is simple their understanding, from mathematical point of view, remains fundamentally incomplete. Anyway the study of this equations has stipulated and influenced treatment, improved and refined the methods of research in partial differential equations.
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Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Conference proceedings. Papers Table of contents 23 papers About About these proceedings Table of contents Search within book.
Offers end pm EST. Originally published in , the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible.
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ReplyNavier–Stokes Equations: Theory and Numerical Analysis. About this Title. Roger Temam, Indiana University, Bloomington, IN. Publication: AMS Chelsea.
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