On the Cauchy Problem for the Zakharov System

@article{Ginibre1997OnTC,
  title={On the Cauchy Problem for the Zakharov System},
  author={Jean Ginibre and Yoshio Tsutsumi and Giorgio Velo},
  journal={Journal of Functional Analysis},
  year={1997},
  volume={151},
  pages={384-436}
}
Abstract We study the local Cauchy problem in time for the Zakharov system, (1.1) and (1.2), governing Langmuir turbulence, with initial data ( u (0), n (0), ∂ t n (0))∈ H k ⊕ H lscr; ⊕ H l−1 , in arbitrary space dimension ν . We define a natural notion of criticality according to which the critical values of ( k , l) are ( ν /2−3/2, ν /2−2). Using a method recently developed by Bourgain, we prove that the Zakharov system is locally well posed for a variety of values of ( k , l). The results… 
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