Preprint 2002-001

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.

Paper:

Available as PostScript (2.2 Mbytes), gzipped PostScript (742 Kbytes; uncompress using gunzip), or PDF (1.0 Mbyte).

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.

Comments:

Submitted by:

<dwang@math.pitt.edu> 11 January 2002.