We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering
toward a weighted average heading. We consider the class of so-called $ p $-alignment …

We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment
system with measure-valued density, bounded velocity, and locally integrable …

We consider the pressureless Euler–Poisson equations with quadratic confinement. For
spatial dimension d≥ 2, d≠ 4, we give a necessary and sufficient condition for the existence …

We prove that certain types of measure-valued map**s are monokinetic ie the distribution
of velocity is concentrated in a Dirac mass. These include weak measure-valued solutions to …

We study the global wellposedness of pressureless Eulerian dynamics in multidimensions,
with radially symmetric data. Compared with the one-dimensional system, a major difference …

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 …

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with
singular communication weights ϕ α (x)=| x|− α for some α> 0. We consider a kinetic BGK …

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 …

arxiv:1905.05090v1 [math.AP] 13 May 2019 Page 1 arxiv:1905.05090v1 [math.AP] 13 May
2019 A SHARP CRITICAL THRESHOLD FOR A TRAFFIC FLOW MODEL WITH LOOK-AHEAD …

We investigate global solutions to the Euler-alignment system in dimensions with
unidirectional flows and strongly singular communication protocols for. Our paper …