On global solutions to a nonlinear Alfvén wave equation

• Autorzy: XS. Feng , F. Wei
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 35Q20: Boltzmann equations
• 35D99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 2
• Strony: 155-172

Daty

wydano

1995

otrzymano

1994-11-20

Twórcy

autor

XS. Feng

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

autor

F. Wei

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

Bibliografia

• [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.