On the regularity of solutions to the k-generalized Korteweg-de Vries equation

2016/06/12 by Kenig, Carlos E., Linares, Felipe, Ponce, Gustavo +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35Q53. Secondary: 35B05

paper · doi:10.48550/arxiv.1606.03715

Abstract

This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In \citeIsazaLinaresPonce it was established that if the initial datun u₀∈ H^l((b,∞)) for some l∈\mathbb Z⁺ and b∈ \mathbb R, then the corresponding solution u(⋅,t) belongs to H^l((β,∞)) for any β∈ \mathbb R and any t∈ (0,T). Our goal here is to extend this result to the case where l∈ \mathbb R⁺.

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