Global well-posedness below energy space for the 1D Zakharov system

Details Global well-posedness below energy space for the 1D Zakharov system Global well-posedness below energy space for the 1D Zakharov system

2000-05-03

arxiv.org/abs/math/0005030v5

Mathematics

Analysis of PDEs

Scientific paper

The Cauchy problem for the 1-dimensional Zakharov system is shown to be
globally well-posed for large data which not necessarily have finite energy.
The proof combines the local well-posedness result of Ginibre, Tsutsumi, Velo
and a general method introduced by Bourgain to prove a similar result for
nonlinear Schr\"odinger equations.

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