English

Minimal mass blow-up solutions for nonlinear Schr\"{o}dinger equations with a potential

Analysis of PDEs 2021-09-20 v4

Abstract

We consider a mass critical nonlinear Schr\"{o}dinger equation with a real-valued potential. In this work, we construct a minimal mass solution that blows up at finite time, under weaker assumptions on spatial dimensions and potentials than Banica, Carles, and Duyckaerts (2011). Moreover, we show that the blow-up solution converges to a blow-up profile. Furthermore, we improve some parts of the arguments in Rapha\"{e}l and Szeftel (2011) and Le Coz, Martel, and Rapha\"{e}l (2016).

Keywords

Cite

@article{arxiv.2007.15968,
  title  = {Minimal mass blow-up solutions for nonlinear Schr\"{o}dinger equations with a potential},
  author = {Naoki Matsui},
  journal= {arXiv preprint arXiv:2007.15968},
  year   = {2021}
}