Norm-inflation results for the BBM equation

2015/11/06 by Bona, Jerry, Dai, Mimi
#35Q35 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.02207

Abstract

Considered here is the periodic initial-value probem for the regularized long-wave (BBM) equation u_t+u_x+uu_x-u_xxt=0. Adding to previous work in the literature, it is shown here that for any s < 0, there is smooth initial data that is small in the L₂-based Sobolev spaces H^s, but the solution emanating from it becomes arbitrarily large in arbitrarily small time. This so called \it norm inflation result has as a consequence the previously determined conclusion that this problem is ill-posed in these negative-norm spaces.

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