### The Cauchy Problem for the Euler Equations for Compressible Fluids

Gui-Qiang Chen and Dehua Wang

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.

Paper:
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Author(s):
Gui-Qiang Chen, <gqchen@math.northwestern.edu>
Dehua Wang, <dwang@math.pitt.edu>
Publishing information:
To appear in the Handbook of Mathematical Fluid Dynamics, Vol. 1, Elsevier, 2002.