Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$
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.
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Author
Colliander, J.;
Holmer, Justin;
Vişan, MonicaISTA;
Zhang, Xiaoyi
Abstract
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.
Mathematics Subject Classification
Publishing Year
Date Published
2008-03-01
Journal Title
Communications on Pure and Applied Analysis
Publisher
American Institute of Mathematical Sciences
Volume
7
Issue
3
Page
467-489
ISSN
eISSN
IST-REx-ID
Cite this
Colliander J, Holmer J, Vişan M, Zhang X. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure and Applied Analysis. 2008;7(3):467-489. doi:10.3934/cpaa.2008.7.467
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. American Institute of Mathematical Sciences. https://doi.org/10.3934/cpaa.2008.7.467
Colliander, J., Justin Holmer, Monica Vişan, and Xiaoyi Zhang. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” Communications on Pure and Applied Analysis. American Institute of Mathematical Sciences, 2008. https://doi.org/10.3934/cpaa.2008.7.467.
J. Colliander, J. Holmer, M. Vişan, and X. Zhang, “Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$,” Communications on Pure and Applied Analysis, 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 $R$.” Communications on Pure and Applied Analysis, vol. 7, no. 3, American Institute of Mathematical Sciences, 2008, pp. 467–89, doi:10.3934/cpaa.2008.7.467.
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