ArticleOriginal scientific text

Title

On global solutions to a nonlinear Alfvén wave equation

Authors 1, 1

Affiliations

  1. Numerical Laboratory for Heliospheric Physics, Chinese Academy of Sciences, P.O. Box 8701, Beijing 100080, China

Abstract

We establish the global existence and uniqueness of smooth solutions to a nonlinear Alfvén wave equation arising in a finite-beta plasma. In addition, the spatial asymptotic behavior of the solution is discussed.

Keywords

nonlinear Alfvén wave, existence and uniqueness of global solution, spatial asymptotic behavior

Bibliography

  1. C. A. Bardos, Regularity theorem for parabolic equations, J. Funct. Anal. 7 (1971), 311-322.
  2. XS. Feng, The existence of global weak solutions for the equation of ion acoustic waves with Landau damping, Math. Appl. 7 (1994), 230-234 (in Chinese).
  3. XS. Feng, The global Cauchy problem for a nonlinear Schrödinger equation, to appear.
  4. XS. Feng and Y. Han, On the Cauchy problem for the third order Benjamin-Ono equation, J. London Math. Soc., to appear.
  5. N. Hayashi, On the derivative Schrödinger equation, Phys. D 55 (1992), 14-36.
  6. R. J. Iorio, Jr., On the Cauchy problem for the Benjamin-Ono equation, Comm. Partial Differential Equations 11 (1986), 1031-1081.
  7. D. J. Kaup and A. C. Newell, An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys. 19 (1978), 798-801.
  8. C. Kenig, G. Ponce and L. Vega, Small solutions to nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 255-288.
  9. J. L. Lions, Quelques méthodes de résolutions des problèmes aux limites non linéaires, Gauthier-Villars, Paris, 1969.
  10. J. L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, Tome I, Dunod, Paris, 1968.
  11. E. Mjølhus and J. Wyller, Nonlinear Alfvén waves in a finite-beta plasma, J. Plasma Physics 40 (1988), 299-318.
  12. W. A. Strauss, On continuity of functions with values in various Banach spaces, Pacific J. Math. 19 (1966), 543-551.
  13. M. Tsutsumi, Weighted Sobolev spaces, and rapidly descreasing solutions of some nonlinear dispersive wave equations, J. Differential Equations 42 (1981), 260-281.
  14. M. Tsutsumi and I. Fukuda, On solutions of the derivative nonlinear Schrödinger equation, existence and uniqueness theorem, Funkcial. Ekvac. 23 (1980), 259-277.
  15. M. Tsutsumi and I. Fukuda, On solutions of the derivative nonlinear Schrödinger equation, Funkcial. Ekvac. 24 (1981), 85-94.
Pages:
155-172
Main language of publication
English
Received
1994-11-20
Published
1995
Exact and natural sciences