Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space Visan, Monica Zhang, Xiaoyi We prove global well posedness and scattering for the nonlinear Schröodinger equation with power-type nonlinearity (mathematical formular) below the energy space, i.e., for s<1. In [15], J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao established polynomial growth of the Hs/x-norm of the solution, and hence global well posedness for initial data in Hs/x, provided s is sufficiently close to 1. However, their bounds are insufficient to yield scattering. In this paper, we use the a priori interaction Morawetz inequality to show that scattering holds in H^s(R^n) whenever s is larger than some value 0<s0(n,p)<1. Khayyam Publishing 2009 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22085 Vişan M, Zhang X. Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space. <i>Differential and Integral Equations</i>. 2009;22(1/2):99-124. doi:<a href="https://doi.org/10.57262/die/1356038556">10.57262/die/1356038556</a> eng info:eu-repo/semantics/altIdentifier/doi/10.57262/die/1356038556 info:eu-repo/semantics/altIdentifier/issn/0893-4983 info:eu-repo/semantics/altIdentifier/arxiv/math/0606611 info:eu-repo/semantics/openAccess