8 problems

Let $n\geqslant 4$ and consider the Yang–Mills Cauchy problem with regular initial data and critical Sobolev norm $\dot{H}_A^{\frac{n-4}{2}}$. Let the conserved norm be the norm as…

Consider the critical dimension $d=4$ radial Yang–Mills equation … where $\Delta_{(d-2)}=\partial_r^2+\frac{d-3}{r}\partial_r$, and let … be the static instanton profile. Let $t_*$…

For the Yang–Mills system in the energy-supercritical range $d\geq 5$, consider the higher-dimensional Bizoń-Biernat self-similar solution and generic large-data evolutions in the…

Consider the Yang–Mills system in temporal gauge in dimension $d\geq 5$, restricted to the equivariant solution class, and let … where $\phi$ is the Bizoń-Biernat self-similar prof…

Biernat–Bizoń conjecture. Based on numerical simulations, Biernat and Bizoń conjectured that $A_T$ is the generic blowup profile within the equivariant solution class. This conject…

Consider the Yang–Mills equations in $(1+d)$-dimensional Minkowski spacetime with $d\geq 5$, and let the closed-form equivariant self-similar solutions be the solutions described i…

Consider the hyperbolic Yang–Mills equation in $4+1$ dimensions for finite-energy connections, with ground state energy $E_{\mathrm{GS}}$, the energy of the minimal nontrivial harm…

Global singularity conjecture. Global well-posedness fails for this equation, and singularities form.