5 problems

Decay-preserving error estimate. The error satisfies

Consider the fractional Kadomtsev–Petviashvili I (fKP-I) equation with fractional exponent $\alpha=1.5$, and let $c$ denote the speed of a traveling wave. A speed $c^*_{1.5}$ is ca…

Let ${\rm dom}$ be a convex domain, let $s$ satisfy $0<s<1$, and let ${\mathcal H}_h^s$ and ${\mathcal G}_h^s$ denote the fine-grid and two-grid operators, respectively, with mesh…

Criticality conjecture. The case $\alpha=1$ is critical: for sufficiently large $\|u_0\|_{L^1}$, the corresponding solution develops a finite-time blowup.

Consider the Cauchy problem … for $(t,x)\in\mathbb{R}^+\times\mathbb{R}$, where $\mathcal{L}_\lambda$ is the fractional Laplacian defined by … A non-uniqueness conjecture for weak…