Journal of Mathematical Sciences

, Volume 164, Issue 4, pp 531–539 | Cite as

Problem on small motions of ideal rotating relaxing fluid

  • D. A. Zakora


We study an evolution problem on small motions of the ideal rotating relaxing fluid in bounded domains. We begin from the problem posing. Then we reduce the problem to a second-order integrodifferential equation in a Hilbert space. Using this equation, we prove a strong unique solvability problem for the corresponding initial-boundary value problem.


Hilbert Space Cauchy Problem Strong Solution Volterra Integral Equation Small Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. D. Bolgova (Orlova) and N. D. Kopachevsky, “Boundary value problems on small oscillations of an ideal relaxing fluid and its generalizations,” Spectral and Evolution Problems. Part 3. Abstr. Third Crimean Autumn Math. School–Symposium, Simferopol’, 41–42 (1994).Google Scholar
  2. 2.
    N. D. Kopachevsky and S.G. Krein, Operator Approach to Linear Problems of Hydrodynamics. Vol. 2. Nonself-Adjoint Problems for Viscous Fluids, Birkhäuser, Basel–Boston–Berlin (2003).Google Scholar
  3. 3.
    N. D. Kopachevskiĭ, S. G. Kreĭn, and Ngo Zui Kan, Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems [in Russian], Nauka, Moscow (1989).Google Scholar
  4. 4.
    S. G. Kreĭn, Linear Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1967).Google Scholar
  5. 5.
    J. V. Ralston, “On stationary modes in inviscid rotating fluids,” J. Math. Anal. Appl., 44, 366–383 (1973).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    K. Rektoris, Variational Methods in Mathematical Physics and Engineering [Russian translation], Mir, Moscow (1985).Google Scholar
  7. 7.
    D. A. Zakora, “The problem on small motions of ideal relaxing fluid,” Din. Sist., Simferopol’, 20, 104–112 (2006).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.V. I. Vernadskii Tavria National UniversitySimferopol’Ukraine

Personalised recommendations