Global attractor and asymptotic smoothing effects for the weakly damped cubic Schrödinger equation in L(T)
نویسنده
چکیده
We prove that the weakly damped cubic Schrödinger flow in L(T) provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak L(T)-convergence inspired by [18]. Combining the compactness in L(T) of the attractor with the approach developed in [10], we show that the attractor is actually a compact set of H(T). This asymptotic smoothing effect is optimal in view of the regularity of the steady states.
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تاریخ انتشار 2009