# American Institute of Mathematical Sciences

September  2006, 6(5): 979-1000. doi: 10.3934/dcdsb.2006.6.979

## Lagrangian averaging for the 1D compressible Euler equations

 1 Applied Physics and Applied Mathematics, Columbia University, New York NY 10027, United States 2 Department of Mathematics, Stanford University, Stanford CA 94305-2125, United States

Received  June 2005 Revised  March 2006 Published  June 2006

We consider a $1$-dimensional Lagrangian averaged model for an inviscid compressible fluid. As previously introduced in the literature, such equations are designed to model the effect of fluctuations upon the mean flow in compressible fluids. This paper presents a traveling wave analysis and a numerical study for such a model. The discussion is centered around two issues. One relates to the intriguing wave motions supported by this model. The other is the appropriateness of using Lagrangian-averaged models for compressible flow to approximate shock wave solutions of the compressible Euler equations.
Citation: Harish S. Bhat, Razvan C. Fetecau. Lagrangian averaging for the 1D compressible Euler equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 979-1000. doi: 10.3934/dcdsb.2006.6.979
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