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Almost global existence for cubic nonlinear Schrödinger equations in one space dimension

  • Author Bio: E-mail address: murphy@math.berkeley.edu; E-mail address: fabiop@math.princeton.edu
  • * Corresponding author: Jason Murphy

    * Corresponding author: Jason Murphy 
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  • We consider non-gauge-invariant cubic nonlinear Schrödinger equations in one space dimension.We show that initial data of size $\varepsilon$ in a weighted Sobolev space lead to solutions with sharp $L_x^∞$ decay up to time $\exp(C\varepsilon^{-2})$. We also exhibit norm growth beyond this time for a specific choice of nonlinearity.

    Mathematics Subject Classification: Primary:35Q55.


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