On the ill-posedness result for the BBM equation

Original · EN

We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hˢ(), 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 Hˢ() to even D'() at any fixed t>0 small enough. This result is sharp.