Analysis Seminar

Justin ForlanoHeriot-Watt University and The Maxwell Institute
Almost sure global well-posedness for the BBM equation with infinite L^2 initial data
Monday, December 2, 2019 - 2:30pm
Malott 406

In this talk, we discuss the Cauchy problem for the Benjamin-Bona-Mahony equation (BBM) posed on the one-dimensional torus. With respect to random initial data of strictly negative Sobolev regularity, we prove that BBM is almost surely globally well-posed. The argument employs the I-method to obtain an a priori bound on the growth of the `residual' part. We then discuss the stability properties of the solution map in this deterministically ill-posed regime.