5 problems

Consider the defocusing nonlinear wave equation … with dimension $d\geq 3$, and let the initial data be radially symmetric. The scaling-critical initial-data space is…

The systems under consideration are basic field theories with critical well-posedness exponent $s_c$, meaning that the $dot H^{s_c} \times dot H^{s_c-1}$ norm of the initial data i…

Consider the defocusing nonlinear Schrödinger equation … in $\mathbb{R}^d$, with $d\geq 1$ and $\alpha\geq 4/d$. Set $s_c=d/2-2/\alpha$, and let…

Let $n$ be the spatial dimension, let $p_{\mathrm{Str}}(n)$ denote the Strauss exponent, and let $\mu$ be the modulus of continuity in a nonlinearity of the form…

Unconditional uniqueness conjecture. A similar unconditional uniqueness result should hold in this setting: uniqueness should hold for critical solutions in $CH^{\frac n2}$ without…