Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions

Kenig, Carlos; Merle, Frank

doi:10.1090/S0002-9947-09-04722-9

Scattering for $\dot {\mathrm {H}}^{1/2}$ bounded solutions to the cubic, defocusing NLS in 3 dimensions
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by Carlos E. Kenig and Frank Merle PDF

Trans. Amer. Math. Soc. 362 (2010), 1937-1962 Request permission

Abstract:

We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order $1/2$ in its maximal interval of existence, then the interval is infinite and the solution scatters. No radial assumption is made.

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