Stability of energy-critical nonlinear Schrodinger equations in high dimensions Tao, Terence Visan, Monica 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. Texas State University 2005 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22086 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. eng info:eu-repo/semantics/altIdentifier/e-issn/1550-6150 info:eu-repo/semantics/altIdentifier/arxiv/math/0507005 info:eu-repo/semantics/openAccess