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Observability and Mathematics - Fluid Mechanics, Solutions of Navier-Stokes Equations, and Modeling (Hardcover)
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Observability and Mathematics - Fluid Mechanics, Solutions of Navier-Stokes Equations, and Modeling (Hardcover)
Series: Advances in Applied Mathematics
Expected to ship within 12 - 17 working days
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The author approaches an old classic problem - the existence of
solutions of Navier-Stokes equations. The main objective is to
model and derive of equation of continuity, Euler equation of fluid
motion, energy flux equation, Navier-Stokes equations from the
observer point of view and solve classic problem for this
interpretation of fluid motion laws. If we have a piece of metal or
a volume of liquid, the idea impresses itself upon us that it is
divisible without limit, that any part of it, however small, would
again have the same properties. But, wherever the methods of
research in the physics of matter were refined sufficiently, limits
to divisibility were reached that are not due to the inadequacy of
our experiments but to the nature of the subject matter.
Observability in mathematics were developed by the author based on
denial of infinity idea. He introduces observers into arithmetic,
and arithmetic becomes dependent on observers. And after that the
basic mathematical parts also become dependent on observers. This
approach permits to reconsider the fluid motion laws, analyze them
and get solutions of classic problems. Table of Contents 1.
Introduction. 2. Observability and Arithmetic. 3. Observability and
Vector Algebra. 4. Observability and Mathematical Analysis
(Calculus). 5. Classic Fluid Mechanics equations and Observability.
6. Observability and Thermodynamical equations. 7. Observability
and equation of continuity. 8. Observability and Euler equation of
motion of the fluid. 9. Observability and energy flux and moment
flux equations. 10. Observability and incompressible fluids. 11.
Observability and Navier-Stokes equations. 12. Observability and
Relativistic Fluid Mechanics. 13. Appendix: Review of publications
of the Mathematics with Observers. 14. Glossary. Bibliography Index
Biography Boris Khots, DrSci, lives in Iowa, USA, Independent
Researcher. Alma Mater - Moscow State Lomonosov University,
Department of Mathematics and Mechanics (mech-math). Creator of
Observer's Mathematics. Participant of more than 30 Mathematical
international congresses, conferences. In particular, participated
with presentation at International Congresses of Mathematicians on
1998 (Germany), 2002 (China), 2006 (Spain), 2010 (India), 2014
(South Korea). More than 150 mathematical books and papers.
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