Global well-posedness for the Schroedinger equation coupled to a nonlinear oscillator
Alexander Komech and Andrew Komech
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Submission date: 23. Aug. 2006
published in: Russian journal of mathematical physics, 14 (2007) 2, p. 164-173
DOI number (of the published article): 10.1134/S1061920807020057
MSC-Numbers: 37K, 35L, 35Q
Keywords and phrases: Schroedinger equation, nonlinear oscillator, global well-posedness
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The Schrödinger equation with the nonlinearity concentrated at a single point proves to be an interesting and important model for the analysis of long-time behavior of solutions, such as the asymptotic stability of solitary waves and properties of weak global attractors. In this note, we prove global well-posedness of this system in the energy space .