From newton⇔s second law to euler⇔s equations of perfect fluids

Daniel Han-Kwan; Mikaela Iacobelli

doi:10.1090/proc/15349

From newton⇔s second law to euler⇔s equations of perfect fluids

Daniel Han-Kwan
, Mikaela Iacobelli

École Polytechnique

ETH Zurich

Research output: Contribution to journal › Article › peer-review

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].

Original language	English
Pages (from-to)	3045-3061
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	7
DOIs	https://doi.org/10.1090/proc/15349
Publication status	Published - 1 Jul 2021

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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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From newton⇔s second law to euler⇔s equations of perfect fluids

Abstract

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