Skip to main content
SpringerLink
Log in

Partial regularity for two dimensional Landau-Lifshitz equations

  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.

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

Similar content being viewed by others

References

  1. Landau L, Lifshitz E-M. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys Z Sowj, 1935, 8:153. Reproduced in Collected Papers of L D Landau, New York: Pergamon Press 1965, 101–114.

    MATH  Google Scholar 

  2. Fogedby H C. Theoretical aspects of mainly low dimensional magnetic systems. Lect Notes Phys, Vol. 131, Berlin, Heidelberg, New York: Springer, 1980

    Google Scholar 

  3. Nakamura K, Sasada T. Soliton and wave trains in ferromagnets. Phys Lett. 1974, 48(A): 321–322

    Google Scholar 

  4. Tjon J, Wright J. Soliton in the continuous heisenberg chain. Phys Rev, 1977, 15B(7): 3470–3476

    Google Scholar 

  5. Chen Y, Guo B. Landau-Lifshitz equation from Riemannian Surfaces. J. PDE, 1996, 9(4): 313–322

    MATH  MathSciNet  Google Scholar 

  6. Guo B, Hong M C. The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps. Calc Var, 1993, 1: 311–334

    Article  MATH  MathSciNet  Google Scholar 

  7. Zhou Y, Guo B, Tan S. Existence and uniqueness of smooth solution for system of ferromagnetic chain. Scienta Sinica, Ser A 1991, 34(3): 257–266

    MATH  MathSciNet  Google Scholar 

  8. Zhou Y, Guo B. Weak solution of system of ferromagnetic chain with several variables. Scienta Sinica, Ser. A 1987, 30(12): 1251–1266.

    MATH  MathSciNet  Google Scholar 

  9. Wang Y D. Heisenberg chain systems from compact manifolds intoS 2. J Math Phys, to appear

  10. Freire A. Uniqueness for the harmonic map flow in two dimensions. Cal Var PDE, 1995, 3(2): 95–105

    Article  MATH  MathSciNet  Google Scholar 

  11. Iwaniec T, Martin G. Quasireguar mappings in even dimension. Acta Math, 1993, 170(1): 29–81

    Article  MATH  MathSciNet  Google Scholar 

  12. Wente H. An existence theorem for surfaces of constant mean curvature. J Math Anal Appl, 1969, 26(2): 318–344

    Article  MATH  MathSciNet  Google Scholar 

  13. Ladyzhenskaja O, Solonnikov V A, Ural'ceva N N. Linear and quasilinear equations of parabolic type. AMS Transl Math Monogr, 1968

  14. Grisvard P P. Equations differentielles abstraites. Ann Scient Ec Norm Sup 4 serie, 1969, t.2(4): 311–395

    MATH  MathSciNet  Google Scholar 

  15. Hélein F. Regularité des applications faiblement harmoniques entre une surface et une sphere. Comptes Rendus Acad Sci, Serie I, 1990, t.311(9): 519–524

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Chen Yunmei

  2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, 100088, Beijing, China

    Ding Shijin & Guo Boling

Authors
  1. Chen Yunmei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ding Shijin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guo Boling
    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

Yunmei, C., Shijin, D. & Boling, G. Partial regularity for two dimensional Landau-Lifshitz equations. Acta Mathematica Sinica 14, 423–432 (1998). https://doi.org/10.1007/BF02580447

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02580447

Keywords

1991MR Subject Classification

Chinese Library Classification

Search

Navigation