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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

A multidimensional piston problem for the Euler equations for compressible flow

Pages: 361 - 383, Volume 13, Issue 2, July 2005

doi:10.3934/dcds.2005.13.361       Abstract        Full Text (339.9K)       Related Articles

Shuxing Chen - School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China (email)
Gui-Qiang Chen - Institute of Mathematics, Fudan University, Shanghai 200433, China (email)
Zejun Wang - Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China (email)
Dehua Wang - Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States (email)

Abstract: A multidimensional piston problem for the Euler equations for compressible isentropic flow is analyzed. Thepiston initially locates at the origin and experiences compressiveand expansive motions with spherical symmetry. The initialsingularity at the origin is one of the difficulties for thisspherically symmetric piston problem. A local shock front solutionfor the compressive motion is constructed based on thelinearization at an approximate solution and the Newton iteration. A global entropy solution for the piston problem is constructed byusing a shock capturing approach and the method of compensatedcompactness.

Keywords:  Euler equations, piston problem, local solutions, global solutions, entropy, compressive motion, expansive motion, initial singularity, origin.
Mathematics Subject Classification:  35L65, 76N10.

Received: May 2004;      Revised: March 2005;      Published: April 2005.