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Uniform attractors of periodic and asymptotically periodic dynamical systems
On the cauchy problem for the coupled Klein Gordon Schrödinger system with rough data
| 1. | Department of Mathematics, South-west Jiaotong University, Chengdu 610031, China |
$ iu_{t}+u_{x x}=-uv, $
$ v_{t t}-v_{x x}+v=|u|^2,$
$u(0, x)= u_0(x), v(0, x)= v_0(x), v_t(0, x)= v_1(x)$
is locally well-posed for weak initial data $(u_0, v_0, v_1)\in H^s\times H^{s-1/2}\times H^{s-3/2}$ with $s\geq 0$. We use the analogous method for estimate the nonlinear couple terms developed by Bourgain and refined by Kenig, Ponce and Vega.
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