Zero-filter limit for the Camassa-Holm equation in Sobolev spaces

The aim of this paper is to answer the question left in Gui and Liu (2015). We prove that given initial data u0 & ISIN; Hs(R) with s > 32 and for some T > 0, the solution of the Camassa-Holm equation converges strongly in L & INFIN;(0,T; Hs(R)) to the inviscid Burgers equation as the filter parameter & alpha; tends to zero.& COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

The aim of this paper is to answer the question left in Gui and Liu (2015). We prove that given initial data u0 ∈ Hs(R) with s > 32 and for some T > 0, the solution of the Camassa-Holm equation converges strongly in L∞(0,T; Hs(R)) to the inviscid Burgers equation as the filter parameter α tends to zero.