We transpose work by T.Mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger equation (NLS) in 1D. As an application we extend to dimension 1D a result on asymptotic stability of ground states of NLS proved by Cuccagna & Mizumachi for dimensions $\ge 3$
On asymptotic stability in energy space of ground states of NLS in 1D / Cuccagna, Scipio. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 245:3(2008), pp. 653-691. [10.1016/j.jde.2008.02.042]
On asymptotic stability in energy space of ground states of NLS in 1D
CUCCAGNA, Scipio
2008-01-01
Abstract
We transpose work by T.Mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger equation (NLS) in 1D. As an application we extend to dimension 1D a result on asymptotic stability of ground states of NLS proved by Cuccagna & Mizumachi for dimensions $\ge 3$
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