Averaging theorems for conservative systems and the weakly compressible Euler equations

G. Métivier*, S. Schochet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A generic averaging theorem is proven for systems of ODEs with two-time scales that cannot be globally transformed into the usual action-angle variable normal form for such systems. This theorem is shown to apply to certain Fourier-space truncations of the non-isentropic slightly compressible Euler equations of fluid mechanics. For the full Euler equations, we derive formally the generic limit equations and analyze some of their properties. In the one-dimensional case, we prove a generic converic convergence result for the full Euler equations, analogous to the result for ODEs. By making use of special properties of the one-dimensional equations, we prove convergence to the solution of a more complicated set of averaged equations when the genericity assumptions fail.

Original languageEnglish
Pages (from-to)106-183
Number of pages78
JournalJournal of Differential Equations
Issue number1
StatePublished - 1 Jan 2003


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