On well-posedness of generalized Korteweg-de Vries equation in scale critical ^L^r space

Published 6 Jul 2015 in math.AP | (1507.01323v2)

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.}