On the Instability for the Cubic Nonlinear Schrödinger Equation
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چکیده
We study the flow map associated to the cubic Schrödinger equation in space dimension at least three. We consider initial data of arbitrary size in Hs, where 0 < s < sc, sc the critical index, and perturbations in Hσ , where σ < sc is independent of s. We show an instability mechanism in some Sobolev spaces of order smaller than s. The analysis relies on two features of super-critical geometric optics: creation of oscillation, and ghost effect.
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تاریخ انتشار 2007