We consider the defocusing supercritical generalized Korteweg-de Vries (gKdV) equation partial derivative(t)u + partial derivative(3)(x)u - partial derivative(x)(u(k+1)) = 0, where k > 4 is an even integer number. We show that if the initial data u(0) belongs to H-1 then the corresponding solution is global and scatters in H-1. Our method of proof is inspired on the compactness method introduced by Kenig and Merle.
Large data scattering for the defocusing supercritical generalized KdV equation
N. Visciglia
2018-01-01
Abstract
We consider the defocusing supercritical generalized Korteweg-de Vries (gKdV) equation partial derivative(t)u + partial derivative(3)(x)u - partial derivative(x)(u(k+1)) = 0, where k > 4 is an even integer number. We show that if the initial data u(0) belongs to H-1 then the corresponding solution is global and scatters in H-1. Our method of proof is inspired on the compactness method introduced by Kenig and Merle.File in questo prodotto:
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