The Cauchy Problem for the Euler Equations for Compressible Fluids

Author: Gui-Qiang Chen and Dehua Wang

Title: The Cauchy Problem for the Euler Equations for Compressible Fluids

Abstract
Some recent developments in the study of the Cauchy problem for the Euler equations for compressible fluids are reviewed. The local and global well-posedness for smooth solutions is presented, and the formation of singularity is exhibited; then the local and global well-posedness for discontinuous solutions, including the BV theory and the $L^\infty$ theory, is extensively discussed. Some recent developments in the study of the Euler equations with source terms are also reviewed.

This article has appeared in:
The Handbook on Mathematical Fluid Dynamics , Vol. 1, pages 421-543 (2002), Elsevier Science B. V.

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Author Address
    
    Department of Mathematics
    Northwestern University
    Evanston, IL 60208-2730
    gqchen@math.nwu.edu