Global attractor for weakly damped Nonlinear Schr\"odinger equations in $L^2(\R)$

Luc Molinet (LAGA); Olivier Goubet (LAMFA)

arxiv: 0910.0172 · v1 · submitted 2009-10-01 · 🧮 math.AP

Global attractor for weakly damped Nonlinear Schr\"odinger equations in L²(R)

Olivier Goubet (LAMFA) , Luc Molinet (LAGA) This is my paper

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keywords odingerschrattractordampedflowglobalnonlinearweakly

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We prove that the weakly damped nonlinear Schr\"odinger flow in $L^2(\mathbb{R})$ provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schr\"odinger flow for the weak topology in $L^2(\R)$.

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Global attractor for weakly damped Nonlinear Schr\"odinger equations in L²(R)

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