145 citations · 309 across the 27 of their papers we have counts for
22 papers · 1 filter
Entropic solutions to the 1D pressureless Euler system with nonlocal interactions
Trevor M. Leslie, Changhui Tan
We study weak solutions of the one-dimensional pressureless Euler-Poisson-alignment system. When smooth solutions develop singularities, distributional weak solutions are not uniqu…
Global well-posedness and refined regularity criterion for the uni-directional Euler-alignment system
Yatao Li, Qianyun Miao, Changhui Tan +1
We investigate global solutions to the Euler-alignment system in dimensions with unidirectional flows and strongly singular communication protocols for $α…
Finite- and Infinite-Time Cluster Formation for Alignment Dynamics on the Real Line
Trevor M. Leslie, Changhui Tan
We show that the locations where finite- and infinite-time clustering occurs for the 1D Euler-alignment system can be determined using only the initial data. Our present work provi…
Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment
McKenzie Black, Changhui Tan
We consider the compressible Euler system with a family of nonlinear velocity alignments. The system is a nonlinear extension of the Euler-alignment system in collective dynamics.…
Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment
Xiang Bai, Qianyun Miao, Changhui Tan +1
In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in…
Sharp critical thresholds for a class of nonlocal traffic flow models
Thomas Hamori, Changhui Tan
We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold con…
Critical thresholds in the Euler-Poisson-alignment system
Manas Bhatnagar, Hailiang Liu, Changhui Tan
This paper is concerned with the global wellposedness of the Euler-Poisson-alignment (EPA) system. This system arises from collective dynamics, and features two types of nonlocal i…
Sticky particle Cucker-Smale dynamics and the entropic selection principle for the 1D Euler-alignment system
Trevor M. Leslie, Changhui Tan
We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication pro…
Critical threshold for global regularity of Euler-Monge-Ampère system with radial symmetry
Eitan Tadmor, Changhui Tan
We study the global wellposedness of the Euler-Monge-Ampère (EMA) system. We obtain a sharp, explicit critical threshold in the space of initial configurations which guarantees the…
The Flow of Polynomial Roots Under Differentiation
Alexander Kiselev, Changhui Tan
The question about the behavior of gaps between zeros of polynomials under differentiation is classical and goes back to Marcel Riesz. In this paper, we analyze a nonlocal nonlinea…
Eulerian dynamics in multi-dimensions with radial symmetry
Changhui Tan
We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dim…
On the global classical solution to compressible Euler system with singular velocity alignment
Li Chen, Changhui Tan, Lining Tong
We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establis…
Global regularity for a 1D Euler-alignment system with misalignment
Qianyun Miao, Changhui Tan, Liutang Xue
We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied…
A sharp critical threshold for a traffic flow model with look-ahead dynamics
Yongki Lee, Changhui Tan
We study a nonlocal traffic flow model with an Arrhenius type look-ahead interaction. We show a sharp critical threshold condition on the initial data which distinguishes the globa…
On the Euler-Alignment system with weakly singular communication weights
Changhui Tan
We study the pressureless Euler equations with nonlocal alignment interactions, which arises as a macroscopic representation of complex biological systems modeling animal flocks. F…
Singularity formation for a fluid mechanics model with nonlocal velocity
Changhui Tan
We study a 1D fluid mechanics model with nonlocal velocity. The equation can be viewed as a fractional porous medium flow, a 1D model of the quasi-geostrophic equation, and also a…
Global regularity for 1D Eulerian dynamics with singular interaction forces
Alexander Kiselev, Changhui Tan
The Euler-Poisson-Alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set agents interacting through mutual attraction/repulsion…
Global regularity for the fractional Euler alignment system
Tam Do, Alexander Kiselev, Lenya Ryzhik +1
We study a pressureless Euler system with a nonlinear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the se…
Finite time blow up in the hyperbolic Boussinesq system
Alexander Kiselev, Changhui Tan
In recent work of Luo and Hou, a new scenario for finite time blow up in solutions of 3D Euler equation has been proposed. The scenario involves a ring of hyperbolic points of the…
First-order aggregation models with alignment
Razvan C. Fetecau, Weiran Sun, Changhui Tan
We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the eq…
Critical thresholds in 1D Euler equations with nonlocal forces
José A. Carrillo, Young-Pil Choi, Eitan Tadmor +1
We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in veloci…
Critical thresholds in flocking hydrodynamics\\with nonlocal alignment
Eitan Tadmor, Changhui Tan
We study the large-time behavior of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dy…