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dc.contributor.authorBoussaid, Nabile
dc.date.accessioned2010-02-02T14:28:59Z
dc.date.available2010-02-02T14:28:59Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3216
dc.language.isoenen
dc.subjectStanding wavesen
dc.subjectStationary solutionsen
dc.subjectSmoothness estimatesen
dc.subjectStrichartz estimatesen
dc.subjectAsymptotic stabilityen
dc.subjectOrbital instabilityen
dc.subjectStabilizationen
dc.subjectNon linear scatteringen
dc.subjectNon linear Dirac equationen
dc.subject.ddc515en
dc.titleOn the asymptotic stability of small nonlinear Dirac standing waves in a resonant caseen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the behavior of perturbations of small nonlinear Dirac standing waves. We assume that the linear Dirac operator of reference $H=D_m+V$ has only two double eigenvalues and that degeneracies are due to a symmetry of $H$ (theorem of Kramers). In this case, we can build a small $4$-dimensional manifold of stationary solutions tangent to the first eigenspace of $H$. Then we assume that a resonance condition holds and we build a center manifold of real codimension $8$ around each stationary solution. Inside this center manifold any $H^{s}$ perturbation of stationary solutions, with $s>2$, stabilizes towards a standing wave. We also build center-stable and center-unstable manifolds each one of real codimension $4$. Inside each of these manifolds, we obtain stabilization towards the center manifold in one direction of time, while in the other, we have instability. Eventually, outside all these manifolds, we have instability in the two directions of time. For localized perturbations inside the center manifold, we obtain a nonlinear scattering result.en
dc.relation.isversionofjnlnameSIAM journal on mathematical analysis
dc.relation.isversionofjnlvol40en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages1621-1670en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/070684641
dc.identifier.urlsitehttp://arxiv.org/abs/math/0611779v2
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSociety for Industrial and Applied Mathematics,en
dc.subject.ddclabelAnalyseen


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