AI 中文总结
本文在临界Besov空间中证明可压缩Navier-Stokes-Vlasov-Fokker-Planck系统强解的存在唯一性，建立一致正则性估计并验证以O(ε)速率收敛的消失粘性极限，同时获得最优时间衰减率。
AI 中文摘要
我们在临界正则性下研究多维可压缩流体-粒子系统，其中载流体与具有Fokker-Planck扩散的粒子相通过阻力耦合。我们证明了在各自临界Besov空间中，Navier-Stokes-Vlasov-Fokker-Planck和Euler-Vlasov-Fokker-Planck系统在平衡态附近的Cauchy问题强解的存在性和唯一性。此外，我们建立了Navier-Stokes-Vlasov-Fokker-Planck系统关于公共粘性参数$\mu=\lambda=\varepsilon$的一致正则性估计，并证明了具有收敛速率$\mathcal O(\varepsilon)$的全局时间消失粘性极限。最后，在初始数据的附加低阶Besov假设下，我们获得了两个系统的最优时间衰减估计，并推导出相对速度和分布函数微观部分的增强衰减速率。
英文摘要
We study multidimensional compressible fluid-particle systems at critical regularity, in which a carrier fluid and a particle phase with Fokker-Planck diffusion are coupled through a drag force. We prove the existence and uniqueness of strong solutions for the Cauchy problems of the Navier-Stokes-Vlasov-Fokker-Planck and Euler-Vlasov-Fokker-Planck systems near equilibrium in their respective critical Besov spaces. Moreover, we establish regularity estimates for the Navier-Stokes-Vlasov-Fokker-Planck system uniform with respect to the common viscosity parameter $μ=λ=\varepsilon$ and justify the global-in-time vanishing-viscosity limit with the convergence rate $\mathcal O(\varepsilon)$. Finally, under an additional lower-order Besov assumption on the initial data, we obtain optimal time-decay estimates for both systems and derive enhanced decay rates for the relative velocity and the microscopic part of the distribution function.
Comments52 pages
