Minimal mass blow-up solutions to rough nonlinear Schroedinger equations
Probability
2020-02-25 v1
Abstract
We study the focusing mass-critical rough nonlinear Schroedinger equations, where the stochastic integration is taken in the sense of controlled rough path. We obtain the global well-posedness if the mass of initial data is below that of the ground state. Moreover, the existence of minimal mass blow-up solutions is also obtained in both dimensions one and two. In particular, these yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up of solutions in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schroedinger equations with lower order perturbations.
Keywords
Cite
@article{arxiv.2002.09659,
title = {Minimal mass blow-up solutions to rough nonlinear Schroedinger equations},
author = {Yiming Su and Deng Zhang},
journal= {arXiv preprint arXiv:2002.09659},
year = {2020}
}