Abstract
The purpose of this paper is to study local and global well-posedness of initial value problem for generalized Korteweg-de Vries (gKdV) equation in ^L^r. We show (large data) local well-posedness, small data global well-posedness, and small data scattering for gKdV equation in the scale critical ^L^r space. A key ingredient is a Stein-Tomas type inequality for the Airy equation, which generalizes usual Strichartz estimates for ^L^r-framework.
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