Attractive Riesz potentials acting on hard spheres

具有吸引性Riesz相互作用力的阻尼Euler系统

Damped Euler system with attractive Riesz interaction forces

本文研究周期域上带吸引性Riesz相互作用和线性阻尼的压差Euler方程，建立了平衡态附近的全局适定性，并证明解随时间指数收敛到平衡态。

A family of Riesz distributions for differential forms on Euclidian space

In this paper we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important Riesz distributions acting on functions, where the corresponding operators are $(-Δ)^{-α/2}$, and we develop basic analogous properties with respect to meromorphic continuation, residues, Fourier transforms, and relations to conformal geometry and representations of the conformal group.

中等正则条件下吸引性Riesz势的平均场极限周围的涨落

Fluctuations around the mean-field limit for attractive Riesz potentials in the moderate regime

本文证明中等相互作用粒子系统中，在吸引性亚库仑势下，涨落满足中心极限定理，渐近为高斯分布，通过均方收敛和定量平均场方法实现。

A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem

We prove the stability of the ball as global minimizer of an attractive shape functional under volume constraint, by means of mass transportation arguments. The stability exponent is $1/2$ and it is sharp. Moreover, we use such stability result together with the quantitative (possibly fractional) isoperimetric inequality to prove that the ball is a global minimizer of a shape functional involving both an attractive and a repulsive term with a sufficiently large fixed volume and with a suitable (possibly fractional) perimeter penalization.

Well-posedness and singularity formation for Vlasov--Riesz system

We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb $Φ= (-Δ)^{-1}ρ$, Manev $(-Δ)^{-1} + (-Δ)^{-\frac12}$, and pure Manev $(-Δ)^{-\frac12}$ potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blow-up result of Horst for attractive Vlasov--Poisson…

可压缩纳维-斯托克斯-里斯系统在真空存在下的稳态渐近稳定性

Asymptotic stability of steady states for the compressible Navier-Stokes-Riesz system in the presence of vacuum

本文研究了可压缩纳维-斯托克斯-里斯系统在真空存在下的稳态渐近稳定性，证明了在特定条件下存在唯一的全局时间强解，并建立了稳态的稳定性及收敛速率。