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Critical thresholds in 1D Euler equations with non-local forces

    https://doi.org/10.1142/S0218202516500068Cited by:85 (Source: Crossref)

    We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for the critical threshold to the system without interaction forces leading to a sharp dichotomy condition between global-in-time existence or finite-time blowup of strong solutions. When the interaction forces are considered, we also give a classification of the critical thresholds according to the different type of interaction forces. We also remark on global-in-time existence when the repulsion is modeled by the isothermal pressure law.

    AMSC: 92D25, 35Q35, 76N10
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