Large-data global well-posedness in the three-dimensional supercoulombic regime

Establish global well-posedness for arbitrary large initial data for the three-dimensional Vlasov equation with power-law interaction exponents in the supercoulombic range $2<\alpha\le3$.

Background

The paper proves large-data global well-posedness only in dimensions $d\ge4$ and for exponents $0<\alpha<3$. It explains that the lower-dimensional regime $d\le3$, $0<\alpha\le d$, is only partially understood. In dimension three, the classical Vlasov–Poisson theory covers the range up to the Coulomb exponent, while small-data results cover $2<\alpha<3$; the remaining large-data supercoulombic regime is therefore identified as the principal unresolved case.