The Cauchy Problem for the Euler Equations for Compressible Fluids
Gui-Qiang Chen and Dehua Wang
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.
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- Gui-Qiang Chen,
- Dehua Wang,
- Publishing information:
- To appear in the Handbook of Mathematical
Fluid Dynamics, Vol. 1, Elsevier, 2002.
- Submitted by:
11 January 2002.
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