Skip to main content
SpringerLink
Log in

An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. 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)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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)

    Article  MathSciNet  Google Scholar 

  3. Friedman, A.: Partial differential equations. Malabar, FL: Krieger 1976 (Reprint)

    Google Scholar 

  4. Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr.4, 213–231 (1951)

    MATH  MathSciNet  Google Scholar 

  5. Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'éspace. Acta Math.63, 193–248 (1934)

    Article  MATH  MathSciNet  Google Scholar 

  6. Milani, A., Negro, A.: On the quasi-stationary Maxwell equations with monotone characteristics in a multiply connected domain. J. Math. Anal. Appl.88, 216–230 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  7. Milani, A., Picard, R.: Maxwell's equations in the quasi-static limit. Technical Report No. 3, Dept. of math. University of Wisconsin Milwaukee, (1991–92)

  8. Picard, R.: Ein Randewertproblem für die zeitunabhängigen Maxwellschen Gleichungen mit der Randbedingungn·εE=n·μH=0 in Gebieten beliebigen Zusammenhangs. Appl. Anal.6, 207–221 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  9. Serrin, J.: The initial value problem for the Navier-Stokes equations. In: Langer, R. (ed.) Nonlinear Problems. Proceedings of a Symposium, Madison 1962 pp. 69–98 Madison, WI: University of Wisconsin Press 1963

    Google Scholar 

  10. Sohr, H.: Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes. Math. Z.184, 359–376 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sohr, H., Wahl, W. von: On the singular set and the uniqueness of weak solutions of Navier-Stokes equations. Manuscri. Math.49, 27–59 (1984)

    Article  MATH  Google Scholar 

  12. Shor, H., von Wahl, W. Generic solvability of the equations of Navier-Stokes. Hiroshima Math. J.17, 613–625 (1987)

    MathSciNet  Google Scholar 

  13. Ströhmer, G.: About an initial-boundary value problem from magneto-hydrodynamics. Math. Z.209, 345–362 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  14. Témam, R.: Navier-Stokes equations: Theory and numerical analysis. Amsterdam: North Holland 1979

    MATH  Google Scholar 

  15. Triebel, H.: Interpolation theory, function spaces, differential operators. Amsterdam: North Holland 1978

    Google Scholar 

  16. 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)

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

    Google Scholar 

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

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Iowa, 52242, Iowa City, IA, USA

    Gerhard Ströhmer

Authors
  1. Gerhard Ströhmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ströhmer, G. An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to magneto-hydrodynamics. Math. Z. 213, 373–385 (1993). https://doi.org/10.1007/BF03025726

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03025726

Keywords

Search

Navigation