Chapter 5 The cauchy problem for the Euler equations for compressible fluids - Chen, G; Wang, D (2002)
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∞ theory, is extensively discussed. Some recent developments in the study of the Euler equations with source terms are also reviewed. © 2002 Elsevier B.V. All rights reserved.