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Creators/Authors contains: "Leslie, Trevor M"

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  1. ; (, Journal of Evolution Equations)
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  2. ; (, Communications in Partial Differential Equations)
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  3. ; ; ; (, Advances in Mathematics)
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  4. ; (, Mathematical Models and Methods in Applied Sciences)
    The goal of this paper is to study limiting behavior of a self-organized continuous flock evolving according to the 1D hydrodynamic Euler Alignment model. We provide a series of quantitative estimates that show how far the density of the limiting flock is from a uniform distribution. The key quantity that controls density distortion is the entropy [Formula: see text], and the measure of deviation from uniformity is given by a well-known conserved quantity [Formula: see text], where [Formula: see text] is velocity and [Formula: see text] is the communication operator with kernel [Formula: see text]. The cases of Lipschitz, singular geometric, and topological kernels are covered in the study. 
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