Symmetry problems : : the Navier-Stokes problem /
By: Ramm, A. G. (Alexander G.) [author.].
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mathemathics and statistics: #23.Publisher: [San Rafael, California] : Morgan & Claypool, [2019]Description: 1 PDF (xiv, 71 pages).Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681735061.Other title: Navier-Stokes problem.Subject(s): Helmholtz equation | Navier-Stokes equations | Scattering (Mathematics) | Helmholtz equation | symmetry problems | Navier--Stokes problem | Inverse problem of potential theoryDDC classification: 518/.64 Online resources: Abstract with links to resource | Abstract with links to full text Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE889 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Includes bibliographical references (pages 65-69).
1. Introduction -- 2. Necessary and sufficient conditions for a scatterer to be spherically symmetric -- 2.1. Scattering by potentials -- 2.2. Scattering by obstacles
3. Symmetry problems for the Helmholtz equation -- 3.1. A general symmetry problem -- 3.2. Old symmetry problem -- 3.3. Necessary and sufficient conditions for S to be a sphere -- 3.4. The Pompeiu problem
4. Other symmetry problems -- 4.1. Volume potential -- 4.2. Surface potential -- 4.3. Invisible obstacles
5. Solution to the Navier-Stokes problem -- 5.1. A new approach -- 5.2. Construction of G -- 5.3. Solution to integral equation for v satisfies NS equations -- 5.4. Uniqueness of the solution to the integral equation -- 5.5. Existence of the solution to integral equation -- 5.6. Energy of the solution -- 5.7. Auxiliary estimates -- 5.8. Proof of the uniqueness of the solution -- 5.9. Proof of the existence of the solution -- 5.10. Convolution and positiveness of distributions
6. Inverse problem of potential theory -- 6.1. Statement of the problem -- 6.2. Proofs.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
Compendex
INSPEC
Google scholar
Google book search
This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier-Stokes problem in R3. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier-Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.
Also available in print.
Title from PDF title page (viewed on April 2, 2019).
There are no comments for this item.