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| So far, only two blow-up regimes have been studied for NLS equations: the pseudo-conformal regime, where the blow-up speed is like $|t| ^{-1}$ and the log-log regime where the blow-up speed is like $|t|^{-1/2}$ with a log-log correction.
In this talk, we consider the nonlinear Schrodinger with a double power nonlinearity where one of the power is L2 critical and the other one is L2-subcritical. We construct a minimal mass blowing up solution whose blow-up speed is neither the log-log speed nor the pseudo-conformal speed, but is of the type $|t|^{-s}$ with $s$ varying between $1/2$ and $1$ depending on the subcritical power. This is based on a joint work with Yvan Martel and Pierre Raphael. |
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