Well posedness and smoothing effect of Schrödinger-Poisson equation

Well posedness and smoothing effect of Schrödinger-Poisson equation

Well-Posedness and Smoothing Effect for Nonlinear Dispersive Equations

where α is a real constant with 2α/3 ̸∈ Z and T > 0. In (1), all the parameters are normalized except for α. Equation (1) appears as a mathematical model for nonlinear pulse propagation phenomena in various fields of physics, especially in nonlinear optics (see [54], [27] and [1]). So far, equation (1) without the third order derivative, that is, the cubic NLS equation has attracted much mathema...

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...

Almost Surely Local Well-posedness of the Cubic Nonlinear Schrödinger Equation below L²(t)

We consider the local well-posedness of the periodic cubic nonlinear Schrödinger equation with initial data below L(T). In particular, we prove that it is locally well-posed almost surely for the initial data in the support of the Gaussian measures on H(T) for each s > − 1 8 .