RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2014, Volume 26, Issue 6, Pages 172–197 (Mi aa1412)

Research Papers

On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations

Sh. Sahaev, V. A. Solonnikov

St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia

Abstract: The paper is concerned with a linear system of Fredholm–Volterra singular integral equations arising in the study of a linearized initial-boundary value problem of magnetohydrodymnamics for a fluid surrounded by an infinite vacuum region. It is proved that this system is solvable in the class of continuous functions satisfying the Hölder condition with respect to the spatial variables, which yields a classical solution of the problem in question.

Keywords: Fredholm–Volterra singular integral equations, classical solution.

Full text: PDF file (283 kB)
References: PDF file   HTML file

English version:
St. Petersburg Mathematical Journal, 2015, 26:6, 985–1003

Bibliographic databases:

Language:

Citation: Sh. Sahaev, V. A. Solonnikov, “On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations”, Algebra i Analiz, 26:6 (2014), 172–197; St. Petersburg Math. J., 26:6 (2015), 985–1003

Citation in format AMSBIB
\Bibitem{SakSol14} \by Sh.~Sahaev, V.~A.~Solonnikov \paper On the proof of the solvability of a~linear problem arising in magnetohydrodynamics with the method of integral equations \jour Algebra i Analiz \yr 2014 \vol 26 \issue 6 \pages 172--197 \mathnet{http://mi.mathnet.ru/aa1412} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3443262} \elib{https://elibrary.ru/item.asp?id=22834114} \transl \jour St. Petersburg Math. J. \yr 2015 \vol 26 \issue 6 \pages 985--1003 \crossref{https://doi.org/10.1090/spmj/1371} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000369702700009} \elib{https://elibrary.ru/item.asp?id=24961513} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944312341} 

• http://mi.mathnet.ru/eng/aa1412
• http://mi.mathnet.ru/eng/aa/v26/i6/p172

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Khompysh Kh., Sakhaev Sh.S., “on Estimates of Solutions of the Linear Stationary Problem of Magnetohydrodynamics Problem in Sobolev Spaces”, Advancements in Mathematical Sciences (Ams 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020033
2. Sh. Sakhaev, “Estimates of a single problem of electrodynamics arising in magnetic hydrodynamics in space $W_{p}^{2,1} (Q_{T} ), p>1$”, Sib. elektron. matem. izv., 17 (2020), 1787–1796
•  Number of views: This page: 223 Full text: 65 References: 27 First page: 36