Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Russian Mathematical Surveys, 2014, Volume 69, Issue 2, Pages 189–207
DOI: https://doi.org/10.1070/RM2014v069n02ABEH004886 (Mi rm9578) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Non-uniqueness for the Euler equations: the effect of the boundary

C. Bardosa, L. Székelyhidi, Jr.b, E. Wiedemanncd

a Université Paris VII – Denis Diderot, Paris, France
b Universität Leipzig, Mathematisches Institut, Leipzig, Germany
c University of British Columbia, Vancouver, Canada
d Pacific Institute for the Mathematical Science, Vancouver, Canada
English version PDF (541 kB) Citations (23)
References:
PDF
HTML
DOI: https://doi.org/10.1070/RM2014v069n02ABEH004886
Abstract: Rotational initial data is considered for the two-dimensional incompressible Euler equations on an annulus. With use of the convex integration framework it is shown that there exist infinitely many admissible weak solutions (that is, with non-increasing energy) for such initial data. As a consequence, on bounded domains there exist admissible weak solutions which are not dissipative in the sense of Lions, as opposed to the case without physical boundaries. Moreover, it is shown that admissible solutions are dissipative if they are Hölder continuous near the boundary of the domain.
Bibliography: 34 titles.
Keywords: Euler equations, non-uniqueness, wild solutions, dissipative solutions, boundary effects, convex integration, inviscid limit, rotational flows.
Funding agency Grant number
European Research Council 277993
Fondation Sciences Mathématiques de Paris
The research of the second author was supported by ERC Grant Agreement No. 277993. Part of this work was done while the third author was a~visitor to the project "Instabilities in Hydrodynamics" of the Fondation Sciences Mathématiques de Paris. He gratefully acknowledges the Fondation's support.
Received: 27.10.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2014, Volume 69, Issue 2(416), Pages 3–22
DOI: https://doi.org/10.4213/rm9578
Bibliographic databases:
Document Type: Article
UDC: 517.958+517.951
MSC: 35D30, 35Q35, 76B03
Language: English
Original paper language: Russian
Citation: C. Bardos, L. Székelyhidi, Jr., E. Wiedemann, “Non-uniqueness for the Euler equations: the effect of the boundary”, Uspekhi Mat. Nauk, 69:2(416) (2014), 3–22; Russian Math. Surveys, 69:2 (2014), 189–207
Citation in format AMSBIB
\Bibitem{BarSzeWie14}
\by C.~Bardos, L.~Sz\'ekelyhidi, Jr., E.~Wiedemann
\paper Non-uniqueness for the Euler equations: the~effect of the boundary
\jour Uspekhi Mat. Nauk
\yr 2014
\vol 69
\issue 2(416)
\pages 3--22
\mathnet{http://mi.mathnet.ru/rm9578}
\crossref{https://doi.org/10.4213/rm9578}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3236935}
\zmath{https://zbmath.org/?q=an:1301.35097}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014RuMaS..69..189B}
\elib{https://elibrary.ru/item.asp?id=21826571}
\transl
\jour Russian Math. Surveys
\yr 2014
\vol 69
\issue 2
\pages 189--207
\crossref{https://doi.org/10.1070/RM2014v069n02ABEH004886}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000338728500001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904304977}
Linking options:
  • https://www.mathnet.ru/eng/rm9578
  • https://doi.org/10.1070/RM2014v069n02ABEH004886
  • https://www.mathnet.ru/eng/rm/v69/i2/p3
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:799
    Russian version PDF:214
    English version PDF:22
    References:64
    First page:33
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024