4 problems

Let $u$ be a solution of the cubic wave equation on its maximal interval $[0,t_+)$, with initial data in $\mathcal{H}^{1/2}$. Logarithmic critical-norm criterion. There exists…

Let $u$ solve the cubic wave equation on $[0,\infty)$ with initial data $(u_0,u_1)\in\mathcal{H}^{1/2}\cap\mathcal{H}^1$, where $\boldsymbol{u}(t)=(u(t),\partial_tu(t))$ and…

Let $\mathcal{H}^s=\dot H^s(\mathbb{R}^3)\times\dot H^{s-1}(\mathbb{R}^3)$ denote the phase space, and consider initial data for the cubic wave equation. The self-similar profile i…

Global non-scattering solutions conjecture. Let $u$ be a solution of the cubic wave equation with the prescribed initial-data problem, defined for $t\in[0,\infty)$ and not scatteri…