Differential and Integral Equations

Low regularity solutions for a generalized Zakharov system

Nickolay Tzvetkov

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Abstract

Using the method of Bourgain (actually we use techniques developed in the paper of Ginibre, Tsutsumi, Velo (cf. [9])) we prove well-posedness of a generalized Zakharov system, describing the spontaneous generation of magnetic field in a cold plasma, in the framework of classical Sobolev spaces. Using the conservation laws of the system we extend these solutions globally in the energy space.

Article information

Source
Differential Integral Equations Volume 13, Number 4-6 (2000), 423-440.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061233

Mathematical Reviews number (MathSciNet)
MR1750034

Zentralblatt MATH identifier
0978.35056

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35A07 76X05: Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]

Citation

Tzvetkov, Nickolay. Low regularity solutions for a generalized Zakharov system. Differential Integral Equations 13 (2000), no. 4-6, 423--440. https://projecteuclid.org/euclid.die/1356061233.


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