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Symmetry problems : the Navier-Stokes problem

Author: A G Ramm
Publisher: [San Rafael, California] : Morgan & Claypool, [2019]
Series: Synthesis lectures on mathemathics and statistics, #23.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: A G Ramm
ISBN: 1681735067 9781681735061
OCLC Number: 1091193877
Notes: Part of: Synthesis digital library of engineering and computer science.
Title from PDF title page (viewed on April 2, 2019).
Description: 1 online resource (xiv, 71 pages)
Contents: 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.
Series Title: Synthesis lectures on mathemathics and statistics, #23.
Other Titles: Navier-Stokes problem
Responsibility: Alexander G. Ramm.

Abstract:

Gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. Ghe book also gives necessary and sufficient conditions for a domain to be  Read more...

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