A RADON TYPE TRANSFORM RELATED TO THE EULER EQUATIONS FOR IDEAL FLUID

被引：0

作者：

Sharafutdinov, V. A. ^{[1
]}

机构：

[1] Sobolev Inst Math, Pr Koptyuga 4, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2023年 / 20卷 / 02期

关键词：

Euler equations; Nadirashvili; Vladuts transform; tensor tomography; FLOW;

D O I：

10.33048/semi.2023.020.054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Nadirashvili - Vladuts transform N that integrates second rank tensor fields f on Rn over hyperplanes. More precisely, for a hyperplane P and vector. parallel to P, Nf(P,.) is the integral of the function fij(x). i.j over P, where. is the unit normal vector to P. We prove that, given a vector field v, the tensor field 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, xi) determined by a solution to the Euler equations. The function w solves some 4th order PDE. We describe all solutions to the latter equation.

引用

页码：880 / 912

页数：33

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