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A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…

Analysis of PDEs · Mathematics 2015-12-04 Ansgar Jüngel , Nicola Zamponi

We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…

Analysis of PDEs · Mathematics 2021-12-28 Jan Haskovec

We consider the Cucker-Smale system with multiplicative noise in a harmonic potential field and investigate the effect of harmonic potential field. In the presence of external potential force, the system is expected to emerge into almost…

Dynamical Systems · Mathematics 2022-05-27 Du Linglong , Zhou Xinyun

This paper is devoted to global existence of weak solutions to the following degenerate kinetic model of chemotaxis \begin{equation} \begin{cases}\label{chemo0} u_t=\Delta (\gamma (v)u) \tau v_{t}=\Delta v-v+u \end{cases} \end{equation}in a…

Analysis of PDEs · Mathematics 2020-07-21 Haixia Li , Jie Jiang

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The…

Analysis of PDEs · Mathematics 2012-09-25 John W. Barrett , Endre Süli

In this paper, we study global existence and large time behaviors of strong solutions to the kinetic Cucker--Smale model coupled with the three dimensional incompressible Navier--Stokes equations in the whole space. Using the maximal…

Analysis of PDEs · Mathematics 2021-12-28 Chunyin Jin

The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the $q$-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different…

Analysis of PDEs · Mathematics 2022-10-12 Piotr B. Mucha , Jan Peszek

In this paper, we study the nonlinear Vlasov-Fokker-Planck equation with fixed collision frequency. We establish the global-in-time existence of weak solutions to the equation with large initial data. Moreover, we show that our solution…

Analysis of PDEs · Mathematics 2024-07-18 Young-Pil Choi , Byung-Hoon Hwang , Yeongseok Yoo

The study of collective behavior in multi-agent systems has attracted the attention of many researchers due to its wide range of applications. Among them, the Cucker-Smale model was developed to study the phenomenon of flocking, and various…

Dynamical Systems · Mathematics 2023-08-31 Jong-Ho Kim , Young Ju Lee , Jea-Hyun Park

We aim at proving existence of weak solutions to the stationary compressible Navier-Stokes system coupled with the Allen-Cahn equation. The model is studied in a bounded three dimensional domain with slip boundary conditions for the…

Analysis of PDEs · Mathematics 2015-01-27 Šimon Axmann , Piotr B. Mucha

We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…

Analysis of PDEs · Mathematics 2012-03-01 Mihai Bostan , J. A. Carrillo

We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid $\mathbb{H}^d$ in any dimensions. In a recent work \cite{H-H-K-K-M}, a first-order aggregation model on the hyperboloid was proposed and its emergent dynamics was…

Mathematical Physics · Physics 2021-08-25 Hyunjin Ahn , Seung-Yeal Ha , Hansol Park , Woojoo Shim

In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…

Analysis of PDEs · Mathematics 2021-02-10 Roberto Natalini , Thierry Paul

We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in \cite{STtopo}. While these systems exhibit flocking behavior emerging from purely local…

Analysis of PDEs · Mathematics 2021-07-05 Daniel Lear , David N. Reynolds , Roman Shvydkoy

In this paper we show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a)…

Analysis of PDEs · Mathematics 2021-07-02 Luigi C. Berselli , Alex Kaltenbach , Roger Lewandowski , Michael Růžička

We establish the existence of weak solutions for a nonlocal Klausmeier model within a small time interval $[0, T)$. The Klausmeier model is a coupled, nonlinear system of partial differential equations governing plant biomass and water…

Analysis of PDEs · Mathematics 2024-12-20 Gabriela Jaramillo , Cristian Meraz

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2017-04-06 Fucai Li , Yanmin Mu , Dehua Wang

We present pathwise flocking dynamics and local sensitivity analysis for the Cucker-Smale(C-S) model with random communications and initial data. For the deterministic communications, it is well known that the C-S model can model emergent…

Dynamical Systems · Mathematics 2017-12-13 Seung-Yeal Ha , Shi Jin

In this paper, we establish the existence of a unique "regular" weak solution to turbulent flows governed by a general family of $\alpha$ models with critical regularizations. In particular this family contains the simplified Bardina model…

Analysis of PDEs · Mathematics 2015-05-28 Hani Ali

We consider a hydrodynamic model of self-organized evolution of agents, with singular interaction kernel $\phi_\alpha(x)=1/|x|^{1+\alpha}$ ($0<\alpha<2$), in the presence of an additional external force. Well-posedness results are already…

Analysis of PDEs · Mathematics 2018-12-05 Trevor M. Leslie