최영필 교수

In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized dynamics which is called Motsch-Tadmor model with noises. We present the global existence and uniqueness of classical solutions to the equation around the global Maxwellian in the whole space. For the large-time behavior, we show the algebraic decay rate of solut

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier–Stokes–BGK system consisting of the BGK model of Boltzmann equation and incompressible Navier–Stokes equations coupled through a drag forcing term. This is achieved by combining weak compactness of the particle interaction operator based on Dunford–Pettis theorem, strong compactness of macroscopic fields of the kineti

We establish a quantified overdamped limit for kinetic Vlasov–Fokker–Planck equations with nonlocal interaction forces. We provide explicit bounds on the error between solutions of that kinetic equation and the limiting equation, which is known under the names of aggregation-diffusion equation or McKean–Vlasov equation. Introducing an intermediate system via a coarse-graining map, we quantitatively estimate the error between the spatial densities of the Vlasov–Fokker–Planck equation and the inte

In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov–Poisson or Vlasov–Poisson–Fokker–Planck equation coupled with the incompressible Navier–Stokes system through the drag force. For the proposed kinetic-fluid model, we study the asymptotic regime corresponding to strong local alignment and diffusion forces. Under suitable assumptions on well-prepared initial data, we rigorously derive a cou

In this paper, we analyze the pressureless damped Euler–Riesz equations posed in either \mathbb{R}^d or \mathbb{T}^d . We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state.We also establish large-time behaviors of classical solutions showing the solutions towards the equilibrium as time goes to infinity. For the whole space case, we first show an algebraic decay rate of solutions under additional assumptions on the init

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker--Smale type. The control design consists of a feedback term regulating the distance between each agent and preassigned subset of neighbors. Such a design represents a multidimensional extension of existing control laws for 1D platoon formation control. For the proposed controller, we study consensus emergence, collision-avoidance, a

In this paper, we study Hegselmann–Krause models with a time‐variable time delay. Under appropriate assumptions, we show the exponential asymptotic consensus when the time delay satisfies a suitable smallness assumption. Our main strategies for this are based on Lyapunov functional approach and careful estimates on the trajectories. We then study the mean‐field limit from the many‐individual Hegselmann–Krause equation to the continuity‐type partial differential equation as the number N of indivi