Skip to main content
Log in

About an initial-boundary value problem from magneto-hydrodynamics

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Adams, R.A.: Sobolev spaces. New York: Academic Press 1975

    MATH  Google Scholar 

  2. Agmon, S.: On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems. Commun. Pure Appl. Math.15, 119–147 (1962)

    MATH  MathSciNet  Google Scholar 

  3. Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Commun. Pure Appl. Math.12, 623–727 (1959)

    MATH  MathSciNet  Google Scholar 

  4. Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Commun. Pure Appl. Math.27, 35–92 (1964)

    MathSciNet  Google Scholar 

  5. Alexandrov, A.F., Bogdankevich, L.S., Rukhadze, A.A.: Principles of plasma electrodynamics Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  6. Bassanini, P., Mattioli, N.: Uniqueness of periodic solutions of the linearized quasi-hydrodynamic plasma equations with impedance boundary conditions. J. Appl. Math. Phys.31, 581–591 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  7. Courant, R., Hilbert, D.: Methods of mathematical physics, vol. I. New York: Interscience 1966 (Seventh Printing)

    Google Scholar 

  8. Duvaut, G., Lions, J.L.: Inéquations en thermoelasticité et magnétohydrodynamique. Arch. Ration. Mech. Anal.46, 241–279 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  9. Eisenhart, L.P., An introduction to differential geometry with use of the tensor calculus. Princeton, New Jersey: Princeton University Press 1947

    MATH  Google Scholar 

  10. Eisenhart, L.P.: Riemannian geometry. Princeton, New Jersey: Princeton University Press 1926 (Second Printing 1949)

    MATH  Google Scholar 

  11. Förste, J.: Über die Grundgleichungen der Plasmadynamik auf der Basis der Zweiflüssig-keitstheorie. Z. Angew. Math. Mech.59, 553–558 (1979)

    MATH  MathSciNet  Google Scholar 

  12. Friedrichs, K.O.: Differential forms of Riemannian manifolds. Commun. Pure Appl. Math.8, 551–590 (1955)

    MATH  MathSciNet  Google Scholar 

  13. Friedman, A.: Partial differential equations. Malabar, Florida: Krieger 1983

    Google Scholar 

  14. Galdi, G.P., Rionero, S.: On magnetohydrodynamics in unbounded domains: stability and uniqueness. Ann. Mat. Pura Appl.115, 119–154 (1977)

    Article  MathSciNet  Google Scholar 

  15. Giga, Y., Yoshida, Z.: On the Ohm-Navier-Stokes system in MHD. J. Math. Phys.24, 2860–2864 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  16. Giga, Y., Yoshida, Z.: On the Ohm-Navier-Stokes system in MHD, Commun. Partial Differ. Equations9, 503–522 (1984)

    MATH  MathSciNet  Google Scholar 

  17. Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. Berlin Heidelberg New York: Springer 1983

    MATH  Google Scholar 

  18. Girault, V., Raviart P.A.: Finite element methods for Navier-Stokes equations, Berlin Heidelberg New York: Springer 1986

    MATH  Google Scholar 

  19. Goebel, R.: Über die Existenz klassischer Lösungen semilinearer parabolischer Differentialgleichungen höherer Ordnung. Math. Z.184, 511–532 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kharchenko, A.P.: Existence of statistical solutions of a MHD equations system. Differ. Equations18, 496–502 (1982)

    MATH  Google Scholar 

  21. Ladyzhenskaya, O.A.: Boundary value problems in mathematical physics. Proc. Steklov. Inst. Math.83 (1965)

  22. Ladyzhenskaya, O.A., Solonnikov, V.A.: The solution of certain magnetohydrodynamics problems for an incompressible viscous liquid. Tr. Mat. Inst., Akad. Nauk. SSSR59, 115–187 (1960)

    Google Scholar 

  23. Lassner, G.: Über ein Rand-Anfangswertproblem der Magnetohydrodynamik. Arch. Ration. Mech.25, 388–405 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  24. Mattei, G.: Una introduzione allo studio die modelli di tipo idrodinamico nella fisica matematica dei plasmi. Boll. Unione Mat. Ital., V. Ser.XVII-A 1–24 (1980)

    MathSciNet  Google Scholar 

  25. Picard, R.: Ein Randwertproblem in der Theorie kraftfreier Magnetfelder. Z. Angew. Math. Phys.27, 169–180 (1976)

    Article  MathSciNet  Google Scholar 

  26. Sanchez-Palencia, E.: Existence des solutions de certains problèmes aux limites en magnétohydrodynamique. J. Méc.7 405–426 (1968)

    MATH  MathSciNet  Google Scholar 

  27. Sanchez-Palencia, E.: Existence et unicité de certains écoulements non stationnaires satisfaisant une proprieté de circulation. C.R. Acad. Sci., Paris Sér. A-B266, A683-A685 (1968)

    MathSciNet  Google Scholar 

  28. Sanchez-Palencia, E.: Quelques résultats d'éxistence et d'unicité pour des écoulements magnétohydrodynamiques non stationnaires. J. Méc.8, 509–541 (1969)

    MATH  MathSciNet  Google Scholar 

  29. Sanchez-Palencia, E.: On certain perturbation problems and singular equations of magnetohydrodynamics. J. Math. Anal. Appl.44, 1–27 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  30. Schmidt, P.G.: On a magnetohydrodynamic problem of Euler type. J. Differ. Equations74, 318–335 (1988)

    Article  MATH  Google Scholar 

  31. Sermange, M., Témam, R.: Some mathematical questions related to MHD equations. Commun. Pure Appl. Math.36, 635–664 (1983)

    MATH  Google Scholar 

  32. Simader, C.G., Sohr, H.: The Helmholtz decomposition and related topics. (Preprint)

  33. Stedry, M., Vejvoda, O.: Equations of magnetohydrodynamics of compressible fluid: periodic solution. Apl. Mat.30, 77–91 (1985)

    MATH  MathSciNet  Google Scholar 

  34. Stedry, M., Vejvoda, O.: Equations of magnethydrodynamics: periodic solution. Cas. Pest. Mat.111, 177–184 (1986)

    MATH  MathSciNet  Google Scholar 

  35. Ströhmer, G.: About the eigenfunctions of the curl-operator. (Preprint)

  36. von Wahl, W.: Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen. Nachr. Akad. Wiss. Gött. II. Math.-Phys. Kl. 231–258 (1972)

  37. von Wahl, W.: The equations of Navier-Stokes and abstract parabolic equations. Braunschweig: Vieweg 1985

    Google Scholar 

  38. von Wahl, W.: Abschätzungen für das Neumann-Problem und die Helmholtz-Zerlegung vonL p . Nachr. Akad. Wiss. Gött., II,2 (1990)

  39. von Wahl, W.: Vorlesung über das Aussenraumproblem für die instionäre Gleichung von Navier-Stokes. (Lect. Notes no. 11, SFB 256) Bonn: 1989

  40. Whitham, G.B.: Linear and non-linear waves. New York: Interscience 1974

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ströhmer, G. About an initial-boundary value problem from magneto-hydrodynamics. Math Z 209, 345–362 (1992). https://doi.org/10.1007/BF02570840

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02570840

Keywords

Navigation