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Mathematical Analysis and Numerical Methods for Science and Technology
Robert DautrayJacques-Louis Lions
其他書名
Volume 6 Evolution Problems II
出版Springer Science & Business Media, 2012-12-06
主題Mathematics / Differential Equations / GeneralMathematics / Number SystemsScience / Chemistry / GeneralTechnology & Engineering / Engineering (General)Science / Physics / Mathematical & ComputationalMathematics / Mathematical AnalysisMathematics / Numerical AnalysisMathematics / AppliedComputers / Artificial Intelligence / General
ISBN36425800419783642580048
URLhttp://books.google.com.hk/books?id=khdtCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.