Higher-dimensional non-localized data global well-posedness conjecture

Consider a cubic quasilinear dispersive flow with small initial data in spatial dimension at least two. Higher-dimensional non-localized data global well-posedness conjecture. The flow has a global-in-time scattering solution. In contrast with the one-dimensional case, the source notes that the focusing/defocusing distinction is not required for the small-data semilinear problem, while the quasilinear higher-dimensional problem is the motivating open case.