Year: 2004
Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JPDE-5382
Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 2 : pp. 137–151
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Short and long dispersive waves