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.
@article{bwmeta1.element.bwnjournal-article-apmv62z2p155bwm,
author = {XS. Feng and F. Wei},
title = {On global solutions to a nonlinear Alfv\'en wave equation},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {155-172},
zbl = {0841.35087},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv62z2p155bwm}
}
XS. Feng; F. Wei. On global solutions to a nonlinear Alfvén wave equation. Annales Polonici Mathematici, Tome 62 (1995) pp. 155-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv62z2p155bwm/
[000] [1] C. A. Bardos, Regularity theorem for parabolic equations, J. Funct. Anal. 7 (1971), 311-322. | Zbl 0214.12302
[001] [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). | Zbl 0914.35034
[002] [3] XS. Feng, The global Cauchy problem for a nonlinear Schrödinger equation, to appear. | Zbl 0841.35087
[003] [4] XS. Feng and Y. Han, On the Cauchy problem for the third order Benjamin-Ono equation, J. London Math. Soc., to appear.
[004] [5] N. Hayashi, On the derivative Schrödinger equation, Phys. D 55 (1992), 14-36. | Zbl 0741.35081
[005] [6] R. J. Iorio, Jr., On the Cauchy problem for the Benjamin-Ono equation, Comm. Partial Differential Equations 11 (1986), 1031-1081. | Zbl 0608.35030
[006] [7] D. J. Kaup and A. C. Newell, An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys. 19 (1978), 798-801. | Zbl 0383.35015
[007] [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. | Zbl 0786.35121
[008] [9] J. L. Lions, Quelques méthodes de résolutions des problèmes aux limites non linéaires, Gauthier-Villars, Paris, 1969.
[009] [10] J. L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, Tome I, Dunod, Paris, 1968. | Zbl 0165.10801
[010] [11] E. Mjølhus and J. Wyller, Nonlinear Alfvén waves in a finite-beta plasma, J. Plasma Physics 40 (1988), 299-318.
[011] [12] W. A. Strauss, On continuity of functions with values in various Banach spaces, Pacific J. Math. 19 (1966), 543-551. | Zbl 0185.20103
[012] [13] M. Tsutsumi, Weighted Sobolev spaces, and rapidly descreasing solutions of some nonlinear dispersive wave equations, J. Differential Equations 42 (1981), 260-281. | Zbl 0488.35071
[013] [14] M. Tsutsumi and I. Fukuda, On solutions of the derivative nonlinear Schrödinger equation, existence and uniqueness theorem, Funkcial. Ekvac. 23 (1980), 259-277.
[014] [15] M. Tsutsumi and I. Fukuda, On solutions of the derivative nonlinear Schrödinger equation, Funkcial. Ekvac. 24 (1981), 85-94.