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AuthorDautray, Robert. author
TitleMathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 6 Evolution Problems II / by Robert Dautray, Jacques-Louis Lions
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000
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Descript XII, 486 p. online resource


The object ofthis chapter is to present a certain number ofresults on the linearised Navier-Stokes equations. The Navier-Stokes equations, which describe the motion of a viscous, incompressible fluid were introduced already, from the physical point of view, in ยง1 of Chap. IA. These equations are nonlinear. We study here the equations that emerge on linearisation from the solution (u = 0, p = 0). This is an interesting exercise in its own right. It corresponds to the case of a very slow flow, and also prepares the way for the study of the complete Navier-Stokes equations. This Chap. XIX is made up of two parts, devoted respectively to linearised stationary equations (or Stokes' problem), and to linearised evolution equations. Questions of existence, uniqueness, and regularity of solutions are considered from the variational point of view, making use of general results proved elsewhere. The functional spaces introduced for this purpose are themselves of interest and are therefore studied comprehensively


XIX. The Linearised Navier-Stokes Equations -- ยง1. The Stationary Navier-Stokes Equations: The Linear Case -- ยง2. The Evolutionary Navier-Stokes Equations: The Linear Case -- ยง3. Additional Results and Review -- XX. Numerical Methods for Evolution Problems -- ยง1. General Points -- ยง2. Problems of First Order in Time -- ยง3. Problems of Second Order in Time -- ยง4. The Advection Equation -- ยง5. Symmetric Friedrichs Systems -- ยง6. The Transport Equation -- ยง7. Numerical Solution of the Stokes Problem -- XXI. Transport -- ยง1. Introduction. Presentation of Physical Problems -- ยง2. Existence and Uniqueness of Solutions of the Transport Equation -- ยง3. Spectral Theory and Asymptotic Behaviour of the Solutions of Evolution Problems -- ยง4. Explicit Examples -- ยง5. Approximation of the Neutron Transport Equation by the Diffusion Equation -- Perspectives -- Orientation for the Reader -- List of Equations -- Table of Notations -- Cumulative Index of Volumes 1-6 -- of Volumes 1-5

Mathematics Chemometrics Partial differential equations Numerical analysis Physics Applied mathematics Engineering mathematics Computational intelligence Mathematics Partial Differential Equations Numerical Analysis Math. Applications in Chemistry Computational Intelligence Appl.Mathematics/Computational Methods of Engineering Theoretical Mathematical and Computational Physics


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