# On global solutions to a nonlinear Alfvén wave equation

Annales Polonici Mathematici (1995)

- Volume: 62, Issue: 2, page 155-172
- ISSN: 0066-2216

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topXS. Feng, and F. Wei. "On global solutions to a nonlinear Alfvén wave equation." Annales Polonici Mathematici 62.2 (1995): 155-172. <http://eudml.org/doc/262630>.

@article{XS1995,

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.},

author = {XS. Feng, F. Wei},

journal = {Annales Polonici Mathematici},

keywords = {nonlinear Alfvén wave; existence and uniqueness of global solution; spatial asymptotic behavior; finite-beta plasma; Cauchy problem; Hilbert transform; global a priori estimates; existence; uniqueness; asymptotic behaviour},

language = {eng},

number = {2},

pages = {155-172},

title = {On global solutions to a nonlinear Alfvén wave equation},

url = {http://eudml.org/doc/262630},

volume = {62},

year = {1995},

}

TY - JOUR

AU - XS. Feng

AU - F. Wei

TI - On global solutions to a nonlinear Alfvén wave equation

JO - Annales Polonici Mathematici

PY - 1995

VL - 62

IS - 2

SP - 155

EP - 172

AB - 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.

LA - eng

KW - nonlinear Alfvén wave; existence and uniqueness of global solution; spatial asymptotic behavior; finite-beta plasma; Cauchy problem; Hilbert transform; global a priori estimates; existence; uniqueness; asymptotic behaviour

UR - http://eudml.org/doc/262630

ER -

## References

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- [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. Zbl0185.20103
- [13] M. Tsutsumi, Weighted Sobolev spaces, and rapidly descreasing solutions of some nonlinear dispersive wave equations, J. Differential Equations 42 (1981), 260-281. Zbl0488.35071
- [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.

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