Differential and Integral Equations

Low regularity solutions for a generalized Zakharov system

Nickolay Tzvetkov

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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