Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$ Colliander, J. Holmer, Justin Visan, Monica Zhang, Xiaoyi We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori $L_{t,x}^8$ spacetime control on solutions. American Institute of Mathematical Sciences 2008 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22081 Colliander J, Holmer J, Vişan M, Zhang X. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications on Pure and Applied Analysis</i>. 2008;7(3):467-489. doi:<a href="https://doi.org/10.3934/cpaa.2008.7.467">10.3934/cpaa.2008.7.467</a> eng info:eu-repo/semantics/altIdentifier/doi/10.3934/cpaa.2008.7.467 info:eu-repo/semantics/altIdentifier/issn/1534-0392 info:eu-repo/semantics/altIdentifier/e-issn/1553-5258 info:eu-repo/semantics/altIdentifier/arxiv/math/0612452 info:eu-repo/semantics/openAccess