5 problems

Klein–Roudenko–Stoilov's conjecture. Blow-up happens in finite time, and blow-up solutions have some resemblance to being self-similar: the blow-up core forms a rightward-moving se…

Let $u(t)$ solve the two-dimensional generalized Zakharov–Kuznetsov equation. In the $L^2$-critical case, the blow-up core is expected to form a rightward-moving self-similarly res…

Let $u$ be a solution of the Zakharov–Kuznetsov equation, and let the moving region be the region described above in which the solution exhibits almost instantaneous smoothing unde…

Consider the supercritical two-dimensional Zakharov–Kuznetsov equation with $p=4$. Let $u_0\in\mathcal{S}(\mathbb{R}^2)$ have sufficiently large mass and energy and some localizati…

Critical scattering and blow-up conjecture. The sub-threshold solution disperses, whereas the super-threshold solution has the stated finite-time self-similar blow-up behavior. Thi…