An Improvement on the Brézis-Gallouët technique for 2D NLS and 1D half-wave equation

Original · EN

We revise the classical approach by Brézis-Gallouët to prove global well posedness for nonlinear evolution equations. In particular we prove global well--posedness for the quartic NLS posed on general domains Ω in ² with initial data in H²(Ω)∩ H¹₀(Ω), and for the quartic nonlinear half-wave equation on with initial data in H¹().