Daniel Lear

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math.AP2020

Geometric Structure of Mass Concentration Sets for Pressureless Euler Alignment Systems

Daniel Lear, Trevor M. Leslie, Roman Shvydkoy +1

We study the limiting dynamics of the Euler Alignment system with a smooth, heavy-tailed interaction kernel $ϕ$ and unidirectional velocity $u = (u, 0, \dots, 0)$ . We dem…

math.AP2020

Unidirectional flocks in hydrodynamic Euler Alignment system II: Singular models

Daniel Lear, Roman Shvydkoy

In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $ϕ (x) := ∣ x ∣^{- (n + α)}$ for $α\in(0…