Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition

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 Schrödinger Equations with Derivative

We prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in H s , for s > 2/3 for small L 2 data. The result follows from an application of the " I-method ". This method allows to define a modification of the energy norm H 1 that is " almost conserved " and can be used to perform an iteration argument. We also remark that the same argument can be us...

Global Well-posedness for Nonlinear Schrödinger Equations with Energy-critical Damping

We consider the Cauchy problem for the nonlinear Schrödinger equations with energy-critical damping. We prove the existence of global intime solutions for general initial data in the energy space. Our results extend some results from [1, 2].

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