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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A trajectory map for the pressureless Euler equations


Author: Ryan Hynd
Journal: Trans. Amer. Math. Soc. 373 (2020), 6777-6815
MSC (2010): Primary 60B10, 35L04, and, 35Q85
DOI: https://doi.org/10.1090/tran/8118
Published electronically: July 28, 2020
MathSciNet review: 4155191
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Abstract: We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide. The equations of motion are a pair of partial differential equations for the particles’ mass distribution and local velocity. We show that solutions of this system exist for given initial conditions by rephrasing these equations in Lagrangian coordinates and then by solving for the associated trajectory map.


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Additional Information

Ryan Hynd
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104
MR Author ID: 789875

Received by editor(s): February 28, 2019
Published electronically: July 28, 2020
Article copyright: © Copyright 2020 American Mathematical Society