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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by Alex Alaniz - UC Riverside
These are step-by-verifiable-step notes which are designed to help students with a year of calculus based physics who are about to enroll in ordinary differential equations go all the way to doctoral foundations in either mathematics or physics.
by John C. Baez, Mike Stay - arXiv
There is extensive network of analogies between physics, topology, logic and computation. In this paper we make these analogies precise using the concept of 'closed symmetric monoidal category'. We assume no prior knowledge of category theory.
by Roy McWeeny - Learning Development Institute
Contents: Linear vector spaces; Elements of tensor algebra; The tensor calculus (Volume elements, tensor densities, and volume integrals); Applications in Relativity Theory (Elements of special relativity, Tensor form of Maxwell's equations).
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The present volume gives a systematic treatment of potential functions. It has a purpose to serve as an introduction for students and to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications.