Global existence of small classical solutions to nonlinear Schrödinger equations

For instance, for one dimensional Klein-Gordon equations with quadratic or cubic nonlinearities, and small and decaying Cauchy data, one proves that the global solutions (when

Our starting point is the smooth effect estimates for the linear Schrödinger equation in one spatial dimension (cf. [7,13,14,24,34]), from which we get a series of linear estimates

TAFLIN, Wave operators and analytic solutions for systems of systems of nonlinear Klein-Gordon equations and of non-linear Schrödinger equations,

In section 1, we recall briefly the theory of the local Cauchy problem, including smoothness properties and the relevant conservation laws, for the NLS equation in

Dinh, Global existence for the defocusing mass-critical nonlinear fourth-order Schr¨ odinger equation below the energy space, preprint (2017).. Papanicolaou, Self-focusing with

Zhao, Global well-posedness and scattering for the defocusing energy critical nonlinear Schr¨ odinger equations of fourth-order in the radial case, J. Zhao, Global well-posedness

Konotop, Nonlinear modes in a generalized PT -symmetric discrete nonlinear Schr¨ odinger equations, J.. For each line the first plot stands for the initial condition, the second

Abstract This short note studies the problem of a global expansion of local results on existence of strong and classical solutions of Navier-Stokes equations in R 3..