Global well-posedness for the two dimensional Navier-Stokes-Vlasov Equations

TL;DR

This paper proves the global well-posedness of the 2D Navier-Stokes-Vlasov equations using a combination of a priori estimates, characteristic methods, and semigroup analysis.

Contribution

It provides the first rigorous proof of global existence and uniqueness for these coupled equations in two dimensions.

Findings

Established global well-posedness for 2D Navier-Stokes-Vlasov equations

Developed a priori estimates for the coupled system

Applied semigroup analysis to demonstrate solution regularity

Abstract

The global well-posedness for the incompressible Navier-Stokes-Vlasov equations in two spatial dimensions is established by a priori estimates, the characteristic method and the semigroup analysis.