On the ill-posedness result for the BBM equation

2010/03/31 by Panthee, Mahendra · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1003.6098

Abstract

We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in H^s(\R), s<0 in the sense that the flow-map u₀↦ u(t) that associates to initial data u₀ the solution u cannot be continuous at the origin from H^s(\R) to even D'(\R) at any fixed t>0 small enough. This result is sharp.

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• Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation

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