Abstract : In this work, our goal is to study the Cauchy problem for some generalization of the following system. iφt + ∆φ = −div(|∇ψ|2∇ψ), ∆ψ = φ. In particular we shall construct solutions in the energy space associ- ated to this system. We give some sufficient conditions on the initial data which ensure that the solutions are global, but we show that in some cases, finite time blow up occures.
Type de document :
Article dans une revue
Differential and integral equations, Khayyam Publishing, 1993, 6 (6), pp.1431-1450
https://hal.inria.fr/hal-00848088
Contributeur : Thierry Colin
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Soumis le : jeudi 25 juillet 2013 - 14:02:33
Dernière modification le : jeudi 14 février 2019 - 14:34:02
Document(s) archivé(s) le : samedi 26 octobre 2013 - 04:25:27
Thierry Colin. On the Cauchy problem for a nonlocal, nonlinear Schrödinger equation occuring in plasma Physics, Differential and Integral Equations. Differential and integral equations, Khayyam Publishing, 1993, 6 (6), pp.1431-1450. 〈hal-00848088〉
