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

Hartmut Pecher
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Abstract

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 Schrödinger equations.

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Hartmut Pecher. 2000-12-27. Global well-posedness below energy space for the 1D Zakharov system. https://arxiv.org/abs/math/0005030

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