article published yes J. Colliander author Justin Holmer author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca Xiaoyi Zhang author 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 Sciences2008 eng 1534-0392 1553-5258 math/061245210.3934/cpaa.2008.7.467 73467-489 yes Colliander, J., Justin Holmer, Monica Vişan, and Xiaoyi Zhang. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>. American Institute of Mathematical Sciences, 2008. <a href="https://doi.org/10.3934/cpaa.2008.7.467">https://doi.org/10.3934/cpaa.2008.7.467</a>. Colliander, J., Holmer, J., Vişan, M., &#38; Zhang, X. (2008). Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications on Pure and Applied Analysis</i>. American Institute of Mathematical Sciences. <a href="https://doi.org/10.3934/cpaa.2008.7.467">https://doi.org/10.3934/cpaa.2008.7.467</a> J. Colliander, J. Holmer, M. Vişan, and X. Zhang, “Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$,” <i>Communications on Pure and Applied Analysis</i>, vol. 7, no. 3. American Institute of Mathematical Sciences, pp. 467–489, 2008. Colliander J, Holmer J, Vişan M, Zhang X. 2008. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure and Applied Analysis. 7(3), 467–489. Colliander, J., et al. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>, vol. 7, no. 3, American Institute of Mathematical Sciences, 2008, pp. 467–89, doi:<a href="https://doi.org/10.3934/cpaa.2008.7.467">10.3934/cpaa.2008.7.467</a>. 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> J. Colliander, J. Holmer, M. Vişan, X. Zhang, Communications on Pure and Applied Analysis 7 (2008) 467–489. 220812026-06-19T08:27:11Z2026-07-01T07:05:55Z