6 problems

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…

Consider a one-dimensional dispersive flow on the real line with a cubic conservative nonlinearity and initial data of size $\epsilon \ll 1$. Non-localized data long-time well-posed…

The Intermediate Long Wave equation has small initial data of size $\epsilon$ and dispersion relation … which is KdV-like at low frequencies and Benjamin–Ono-like at high frequencie…

Consider a bounded solution $u$ of the focusing energy-critical nonlinear wave equation (NLW). A soliton resolution conjecture predicts that, as time approaches the maximal time of…

Consider initial data that are the $x$-derivative of a rapidly decreasing smooth function in $L_{2}(\mathbb{R}^{2})$ with a single maximum. Write the two-dimensional dispersionless…

Even-power and independence conjecture. The quasilinear part of an integrable dispersive conservation law contains only even powers of $\epsilon$, and all coefficients of the quasil…