Polynomial Upper Bounds for the Instability of the Nonlinear Schr¨odinger Equation below the Energy Norm

@inproceedings{TakaokaPolynomialUB,
  title={Polynomial Upper Bounds for the Instability of the Nonlinear Schr¨odinger Equation below the Energy Norm},
  author={Hideo Takaoka and Terence Tao}
}
We continue the study (initiated in [18]) of the orbital stability of the ground state cylinder for focussing non-linear Schrödinger equations in the H s (R n) norm for 1 − ε < s < 1, for small ε. In the L 2-subcritical case we obtain a polynomial bound for the time required to move away from the ground state cylinder. If one is only in the H 1-subcritical case then we cannot show this, but for defocussing equations we obtain global well-posedness and polynomial growth of H s norms for s… CONTINUE READING