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Article Contents

# Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm

• We continue the study (initiated in [18]) of the orbital stabilityof the ground state cylinder for focussing non-linear Schrödinger equationsin the $H^s(\R^n)$ norm for $1-\varepsilon < s < 1$, for small $\varepsilon$. In the $L^2$-subcritical case weobtain a polynomial bound for the time required to move away from theground state cylinder. If one is only in the $H^1$-subcritical casethen we cannot show this, but for defocussing equations we obtain global well-posedness andpolynomial growth of $H^s$ norms for $s$ sufficiently close to 1.
Mathematics Subject Classification: 35Q53, 42B35, 37K10.

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