We study the ill-posedness problem for the regularized long-wave equation (Benjamin-Bona-Mahony equation) in the Sobolev space $H^s$ with $s<0$. It is shown that the solution map in $H^s$ is discontinuous at the origin. More precisely, we construct an arbitrarily small initial data such that the solution becomes arbitrarily large instantaneously in $H^s$.
On Special Properties of Solutions to the Benjamin-Bona-Mahony Equation
Continuity of the solution map of some active scalar equations in Hölder and Zygmund spaces
Hölder Continuity of the Data to Solution Map for HR in the Weak Topology
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