GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE DEFOCUSING ENERGY-CRITICAL NONLINEAR SCHRÖDINGER EQUATION IN R1+4 By E. RYCKMAN and M. VISAN
نویسنده
چکیده
We obtain global well-posedness, scattering, uniform regularity, and global L6 t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in R×R4. Our arguments closely follow those of Colliender, Hoel, et al., though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the L6 t,x-norm.
منابع مشابه
6 Global Well - Posedness and Scattering for the Defocusing Energy - Critical Nonlinear Schrödinger Equation in R
We obtain global well-posedness, scattering, uniform regularity, and global L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in R × R. Our arguments closely follow those in [11], though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound o...
متن کاملStability of Energy-critical Nonlinear Schrödinger Equations in High Dimensions Terence Tao and Monica Visan
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, i...
متن کاملStability of Energy-critical Nonlinear Schrödinger Equations in High Dimensions
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, i...
متن کاملGlobal well-posedness and scattering for the energy-critical, defocusing Hartree equation in R
We obtain global well-posedness, scattering, uniform regularity, and global L t L 6n 3n−8 x spacetime bounds for energy-space solutions to the defocusing energycritical nonlinear Hartree equation in R× R, n ≥ 5.
متن کاملGlobal Well-posedness and Scattering for the Mass-critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions
We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation iut + ∆u = |u|4/nu for large spherically symmetric Lx(R n) initial data in dimensions n ≥ 3. After using the reductions in [32] to reduce to eliminating blowup solutions which are almost periodic modulo scaling, we obtain a frequency-localized Morawetz...
متن کامل