5 problems

Consider the mass-critical one-dimensional focusing half-wave equation … where $|D|$ is the Fourier multiplier operator with symbol $|\xi|$. The paper proves an upper bound of log-…

Let $(q,r)$ be an admissible Strichartz pair in dimension $d=1$, and consider the corresponding Schrödinger Strichartz ratio and its extremizers. Universal Gaussian extremizer conj…

Periodic traveling-wave bifurcation conjecture. When the homogeneous ground state destabilizes, a spatially periodic traveling wave of this form bifurcates.

The conjecture. Theorem should remain valid when the initial data are assumed to belong only to $E^1(\mathbb R^2)$.

A soliton is a coherent, non-dispersive solution of a dispersive equation. A global bounded solution is a solution that exists for all $t$ and remains bounded in the relevant norm.…