Scattering for the quartic generalised Korteweg-de Vries equation

2006/05/14 by Tao, Terence · 2 citations
#35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0605357

Abstract

We show that the quartic generalised KdV equation u_t + u_xxx + (u⁴)_x = 0 is globally wellposed for data in the critical (scale-invariant) space H^-1/6_x(\R) with small norm (and locally wellposed for large norm), improving a result of Grünrock. As an application we obtain scattering results in H¹_x(\R) ∩ H^-1/6_x(\R) for the radiation component of a perturbed soliton for this equation, improving the asymptotic stability results of Martel and Merle.

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• On the asymptotic dynamics for the L²-supercritical gKDV equation
• Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation

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