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- W2950555220 abstract "We study the long-time behaviour of the focusing cubic NLS on $R$ in the Sobolev norms $H^s$ for $0 < s < 1$. We obtain polynomial growth-type upper bounds on the $H^s$ norms, and also limit any orbital $H^s$ instability of the ground state to polynomial growth at worst; this is a partial analogue of the $H^1$ orbital stability result of Weinstein. In the sequel to this paper we generalize this result to other nonlinear Schrodinger equations. Our arguments are based on the ``$I$-method'' from our earlier papers, which pushes down from the energy norm, as well as an ``upside-down $I$-method'' which pushes up from the $L^2$ norm." @default.
- W2950555220 created "2019-06-27" @default.
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- W2950555220 date "2002-06-20" @default.
- W2950555220 modified "2023-09-28" @default.
- W2950555220 title "Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm" @default.
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