Navier-Stokes Equations: On the Existence and the Search Method for Global Solutions
by Solomon I. Khmelnik
Publisher: MiC 2011
Number of pages: 105
In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum.
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A set of class notes taken by math graduate students, the goal of the course was to introduce some basic concepts from theoretical physics which play so fundamental role in a recent intermarriage between physics and pure mathematics.
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From the table of contents: The differential equations of mechanics; The three-body problem : simple collisions (The n-body problem); The three-body problem: general collision (Stability theory of solutions of differential equations).
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