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Vladimir I. Arnold,Boris A. Khesin

Topological Methods in Hydrodynamics

Topological Methods in Hydrodynamics

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  • More about Topological Methods in Hydrodynamics

The book is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It is accessible to graduates and pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

Format: Hardback
Length: 455 pages
Publication date: 13 May 2021
Publisher: Springer Nature Switzerland AG

The first comprehensive monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It provides a comprehensive introduction to the necessary preliminary notions in both hydrodynamics and pure mathematics, accompanied by numerous examples and figures. This book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

The book offers a comprehensive treatment of ideal hydrodynamics and magnetohydrodynamics, covering a wide range of topics.

It begins by introducing the fundamental principles of hydrodynamics and pure mathematics, providing a solid foundation for the subsequent discussions.

Throughout the book, numerous examples and figures are used to illustrate the concepts and theories discussed, making it easier for readers to grasp and understand the material.

The book is organized into chapters, each dedicated to a specific topic.

Chapter 1 provides an overview of the basic concepts in hydrodynamics, including fluid dynamics, thermodynamics, and electromagnetism.

Chapter 2 delves into the group-theoretic aspects of ideal hydrodynamics, exploring the symmetry properties of flow fields and the formation of singularities.

Chapter 3 discusses the geometric aspects of ideal hydrodynamics, including the study of manifolds, surfaces, and curves in the context of fluid flow.

Chapter 4 explores the application of ideal hydrodynamics to magnetohydrodynamics, discussing the behavior of magnetic fields in fluids and the formation of magnetic structures.

Chapter 5 discusses the numerical methods used to solve ideal hydrodynamics and magnetohydrodynamics problems, including finite difference and finite element techniques.

Chapter 6 summarizes the key findings and conclusions of the book.

Ideal hydrodynamics and magnetohydrodynamics play a crucial role in many fields, including astrophysics, plasma physics, and engineering.

This book provides a valuable resource for researchers and students interested in these topics, offering a comprehensive and up-to-date treatment of the subject.

In conclusion, Ideal Hydrodynamics and Magnetohydrodynamics: A Unified Point of View is a groundbreaking work that offers a comprehensive and accessible introduction to the topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics.

Weight: 875g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030742775
Edition number: 2nd ed. 2021

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