A Radon type transform related to the Euler equations for ideal fluid Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2023, Volume: 20, Number: 2, Pages: 880-912 Pages count : 33 DOI: 10.33048/semi.2023.20.054 | ||
| Tags | Euler equations, Nadirashvili Vladuts transform, tensor tomography | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
We study the Nadirashvili Vladuts transform N that integrates second rank tensor elds f on Rn over hyperplanes. More precisely, for a hyperplane P and vector η parallel to P, Nf(P,η) is the integral of the function fij(x)ξiηj over P, where ξ is the unit normal vector to P. We prove that, given a vector eld v, the tensor eld f = v ⊗v belongs to the kernel of N if and only if there exists a function p such that (v,p) is a solution to the Euler equations. Then we study the Nadirashvili Vladuts potential w(x,ξ) determined by a solution to the Euler equations. The function w solves some 4th order PDE. We describe all solutions to the latter equation.
Cite:
Sharafutdinov V.A.
A Radon type transform related to the Euler equations for ideal fluid
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №2. С.880-912. DOI: 10.33048/semi.2023.20.054 WOS Scopus РИНЦ
A Radon type transform related to the Euler equations for ideal fluid
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №2. С.880-912. DOI: 10.33048/semi.2023.20.054 WOS Scopus РИНЦ
Dates:
| Submitted: | May 27, 2023 |
| Published print: | Oct 26, 2023 |
| Published online: | Oct 26, 2023 |
Identifiers:
| Web of science: | WOS:001095866000005 |
| Scopus: | 2-s2.0-85176399946 |
| Elibrary: | 82134641 |
Citing:
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