From Newton’s second law to Euler’s equations of perfect fluids

Han-Kwan, Daniel; Iacobelli, Mikaela

doi:10.1090/proc/15349

From Newton’s second law to Euler’s equations of perfect fluids
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by Daniel Han-Kwan and Mikaela Iacobelli PDF

Proc. Amer. Math. Soc. 149 (2021), 3045-3061 Request permission

Abstract:

Vlasov equations can be formally derived from $N$-body dynamics in the mean-field limit. In some suitable singular limits, they may themselves converge to fluid dynamics equations. Motivated by this heuristic, we introduce natural scalings under which the incompressible Euler equations can be rigorously derived from $N$-body dynamics with repulsive Coulomb interaction. Our analysis is based on the modulated energy methods of Brenier and [Comm. Partial Differential Equations 25 (2000), pp. 737–754] Serfaty [Duke Math. J. 169 (2020), pp. 2887–2935].

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