Minimal mass blow up solutions for a double power nonlinear Schr\"odinger equation

@article{Coz2014MinimalMB,
  title={Minimal mass blow up solutions for a double power nonlinear Schr\"odinger equation},
  author={Stefan Le Coz and Yvan Martel and Pierre Raphael},
  journal={arXiv: Analysis of PDEs},
  year={2014}
}
We consider a nonlinear Schr\"odinger equation with double power nonlinearity, where one power is focusing and mass critical and the other mass sub-critical. Classical variational arguments ensure that initial data with mass less than the mass of the ground state of the mass critical problem lead to global in time solutions. We are interested by the threshold dynamic and in particular by the existence of finite time blow up minimal solutions. For the mass critical problem, such an object exists… 
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