The Zakharov system in dimension
Timothy Candy
University of Otago, Dunedin, New ZealandSebastian Herr
Universität Bielefeld, GermanyKenji Nakanishi
Kyoto University, Japan
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Abstract
The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, persistence of initial regularity, and real-analytic dependence on the initial data. In addition, under a condition on the data for the Schrödinger equation at the lowest admissible regularity, global well-posedness and scattering are proved. The results cover energy-critical and energy-supercritical dimensions .
Cite this article
Timothy Candy, Sebastian Herr, Kenji Nakanishi, The Zakharov system in dimension . J. Eur. Math. Soc. 25 (2023), no. 8, pp. 3177–3228
DOI 10.4171/JEMS/1212