@Article{JPDE-17-2,
author = {},
title = {Local Well-posedness of Interaction Equations for Short and Long Dispersive Waves},
journal = {Journal of Partial Differential Equations},
year = {2004},
volume = {17},
number = {2},
pages = {137--151},
abstract = { The well-posedness of the Cauchy problem for the system {i∂_tu + ∂²_xu = uv + |u|²u, t, x ∈ \mathbb{R}, ∂_tv + ∂_xΗ∂_xv = ∂_x|u|², u(0, x) = u_0(x), v(0, x) = v_0(x), is considered. It is proved that there exists a unique local solution (u(x, t), v(x, t)) ∈ C([0, T);H^s) ×C([0, T);H^{s-\frac{1}{2}}) for any initial data (u_0, v_0) ∈ H^s(\mathbb{R}) ×H^{s-\frac{1}{2}} (\mathbb{R})(s ≥ \frac{1}{4}) and the solution depends continuously on the initial data.},
issn = {2079-732X},
doi = {https://doi.org/2004-JPDE-5382},
url = {https://global-sci.com/article/88549/local-well-posedness-of-interaction-equations-for-short-and-long-dispersive-waves}
}