Mathematical Analysis and Numerical Methods for Science and Technology: Volume 6 Evolution Problems II
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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 1 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.
Format:Paperback
Language:English
ISBN:3540661026
ISBN13:9783540661023
Release Date:December 1999
Publisher:Springer
Length:486 Pages
Weight:1.54 lbs.
Dimensions:1.0" x 6.1" x 9.2"
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