2023/03/22 by Kim, Chanwoo, Nguyen, Trinh T.
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2303.12257
A rigorous derivation of point vortex systems from kinetic equations has been a challenging open problem, due to singular layers in the inviscid limit, giving a large velocity gradient in the Boltzmann equations. In this paper, we derive the Helmholtz-Kirchhoff point-vortex system from the hydrodynamic limits of the Boltzmann equations. We construct Boltzmann solutions by the Hilbert-type expansion associated to the point vortices solutions of the 2D Navier-Stokes equations. We give a precise pointwise estimate for the solution of the Boltzmann equations with small Strouhal number and Knudsen number.