[{"OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0507005","open_access":"1"}],"month":"10","date_updated":"2026-07-01T12:31:43Z","das_tickbox":"1","oa_version":"Preprint","article_type":"original","oa":1,"article_processing_charge":"No","abstract":[{"text":"We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3, for solutions which have large, but finite, energy and large, but finite, Strichartz norms. For dimensions n ≤ 6, this theory is a standard extension of the small data well-posedness theory based on iteration in Strichartz spaces. However, in dimensions n > 6 there is an obstruction to this approach because of the subquadratic nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz). We resolve this by iterating in exotic Strichartz spaces instead. The theory developed here will be applied in a subsequent paper of the second author, [21], to establish global well-posedness and scattering for the defocusing energy-critical equation for large energy data.","lang":"eng"}],"day":"26","extern":"1","publisher":"Texas State University","_id":"22086","publication_status":"published","author":[{"last_name":"Tao","first_name":"Terence","full_name":"Tao, Terence"},{"full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"external_id":{"arxiv":["math/0507005"]},"date_published":"2005-10-26T00:00:00Z","arxiv":1,"page":"1-28","intvolume":"      2005","OA_place":"repository","publication_identifier":{"eissn":["1550-6150"]},"mathsc":["35J10"],"volume":2005,"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Tao T, Vişan M. Stability of energy-critical nonlinear Schrodinger equations in high dimensions. <i>Electronic Journal of Differential Equations</i>. 2005;2005(118):1-28.","mla":"Tao, Terence, and Monica Vişan. “Stability of Energy-Critical Nonlinear Schrodinger Equations in High Dimensions.” <i>Electronic Journal of Differential Equations</i>, vol. 2005, no. 118, Texas State University, 2005, pp. 1–28.","ista":"Tao T, Vişan M. 2005. Stability of energy-critical nonlinear Schrodinger equations in high dimensions. Electronic Journal of Differential Equations. 2005(118), 1–28.","short":"T. Tao, M. Vişan, Electronic Journal of Differential Equations 2005 (2005) 1–28.","chicago":"Tao, Terence, and Monica Vişan. “Stability of Energy-Critical Nonlinear Schrodinger Equations in High Dimensions.” <i>Electronic Journal of Differential Equations</i>. Texas State University, 2005.","ieee":"T. Tao and M. Vişan, “Stability of energy-critical nonlinear Schrodinger equations in high dimensions,” <i>Electronic Journal of Differential Equations</i>, vol. 2005, no. 118. Texas State University, pp. 1–28, 2005.","apa":"Tao, T., &#38; Vişan, M. (2005). Stability of energy-critical nonlinear Schrodinger equations in high dimensions. <i>Electronic Journal of Differential Equations</i>. Texas State University."},"scopus_import":"1","quality_controlled":"1","date_created":"2026-06-19T08:44:06Z","title":"Stability of energy-critical nonlinear Schrodinger equations in high dimensions","publication":"Electronic Journal of Differential Equations","language":[{"iso":"eng"}],"year":"2005","issue":"118","type":"journal_article"}]