Tao, TerenceVisan, Monica2021-06-222021-06-222005-10-26Tao, T., & Visan, M. (2005). Stability of energy-critical nonlinear Schrodinger equations in high dimensions. <i>Electronic Journal of Differential Equations, 2005</i>(118), pp. 1-28.1072-6691https://hdl.handle.net/10877/13790We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3, for solutions which have larger, 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.Text28 pages1 file (.pdf)enAttribution 4.0 InternationalLocal well-posednessUniform well-posednessScattering theoryStrichartz estimatesArticle