On the Cauchy problem in Besov spaces for a non-linear Schrödinger equation

  title={On the Cauchy problem in Besov spaces for a non-linear Schr{\"o}dinger equation},
  author={Fabrice Planchon},
We prove that the initial value problem for a non-linear Schrödinger equation is well-posed in the Besov space Ḃ n 2 − 2 α ,∞ 2 (Rn), where the nonlinearity is of type |u|αu. This allows to obtain self-similar solutions, and to recover previous results under weaker smallness assumptions on the data. 

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