LOW REGULARITY WELL–POSEDNESS FOR DISPERSIVE EQUATIONS ON SEMI–INFINITE INTERVALS

We summarize and report recent advancements in the theory of dispersive equations posed on semi–infinite intervals. By employing modern Fourier analysis techniques we show how these initial-boundary value problems can be resolved for initial data in Sobolev spaces of low regularity. In almost all the cases, we obtain sharp results that match the regularity of their full line analogues. We especially address the issues of local well–posedness, nonlinear smoothing, and uniqueness of solutions. In the second part of the paper we apply some of the tools we discussed in the first part, to prove existence and uniqueness of L² solutions for the biharmonic equation, extending the result in [10].