A well-known result of Carrillo, Choi, Tadmor, and Tan [1] states that the 1D Euler Alignment model with smooth interaction kernels possesses a “critical threshold” criterion for the global existence or finite-time blowup of solutions, depending on the global nonnegativity (or lack thereof) of the quantity
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Trevor M. Leslie 1

@article{CRMATH_2020__358_4_421_0, author = {Trevor M. Leslie}, title = {On the {Lagrangian} {Trajectories} for the {One-Dimensional} {Euler} {Alignment} {Model} without {Vacuum} {Velocity}}, journal = {Comptes Rendus. Math\'ematique}, pages = {421--433}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {4}, year = {2020}, doi = {10.5802/crmath.56}, language = {en}, }
TY - JOUR AU - Trevor M. Leslie TI - On the Lagrangian Trajectories for the One-Dimensional Euler Alignment Model without Vacuum Velocity JO - Comptes Rendus. Mathématique PY - 2020 SP - 421 EP - 433 VL - 358 IS - 4 PB - Académie des sciences, Paris DO - 10.5802/crmath.56 LA - en ID - CRMATH_2020__358_4_421_0 ER -
Trevor M. Leslie. On the Lagrangian Trajectories for the One-Dimensional Euler Alignment Model without Vacuum Velocity. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 421-433. doi : 10.5802/crmath.56. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.56/
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