Global well-posedness for the defocussing mass-critical stochastic nonlinear Schrödinger equation on ? at L2 regularity

Global Well - Posedness and Scattering for the Energy - Critical Nonlinear Schrödinger Equation In

We obtain global well-posedness, scattering, and global L10 t,x spacetime bounds for energy-class solutions to the quintic defocusing Schrödinger equation in R1+3, which is energy-critical. In particular, this establishes global existence of classical solutions. Our work extends the results of Bourgain [4] and Grillakis [20], which handled the radial case. The method is similar in spirit to the...

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...

Global Well-posedness for the L2-critical Nonlinear Schrödinger Equation in Higher Dimensions

The initial value problem for the L critical semilinear Schrödinger equation in R, n ≥ 3 is considered. We show that the problem is globally well posed in H(R) when 1 > s > √ 7−1 3 for n = 3, and when 1 > s > −(n−2)+ √ (n−2)+8(n−2) 4 for n ≥ 4. We use the “I-method” combined with a local in time Morawetz estimate.

Low Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data

The Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition is considered. Local well-posedness for data u0 in the space b H r (T), defined by the norms ‖u0‖ b Hs r (T) = ‖〈ξ〉 s b u0‖lr′ ξ , is shown in the parameter range s ≥ 1 2 , 2 > r > 4 3 . The proof is based on an adaptation of the gauge transform to the periodic setting and an appropriate varian...

Global Well - Posedness and Scattering for the Defocusing , L 2 - Critical Nonlinear Schrödinger