TY - JOUR

T1 - Averaging theorems for conservative systems and the weakly compressible Euler equations

AU - Métivier, G.

AU - Schochet, S.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037222786&partnerID=8YFLogxK

U2 - 10.1016/S0022-0396(02)00037-2

DO - 10.1016/S0022-0396(02)00037-2

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AN - SCOPUS:0037222786

VL - 187

SP - 106

EP - 183

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -