Two-dimensional and higher-dimensional quasilinear global well-posedness conjecture

Consider quasilinear dispersive flows in two and higher spatial dimensions with cubic nonlinearities and sufficiently small initial data. Two-dimensional and higher-dimensional quasilinear global well-posedness conjecture. Such flows have global-in-time, scattering solutions. The semilinear small-data problem is described as accessible through Strichartz estimates, whereas the quasilinear problem remains an open class of problems because those estimates are not readily available.