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February  2005, 13(2): 361-383. doi: 10.3934/dcds.2005.13.361

A multidimensional piston problem for the Euler equations for compressible flow

Shuxing Chen 1, , Gui-Qiang Chen 2, , Zejun Wang 3, and  Dehua Wang 4,

1. 

School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China
2. 

Institute of Mathematics, Fudan University, Shanghai 200433, China
3. 

Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China
4. 

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received  May 2004 Revised  March 2005 Published  April 2005

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: entropy, compressive motion, origin., expansive motion, piston problem, initial singularity, local solutions, Euler equations, global solutions.
Mathematics Subject Classification: 35L65, 76N1.
Citation: Shuxing Chen, Gui-Qiang Chen, Zejun Wang, Dehua Wang. A multidimensional piston problem for the Euler equations for compressible flow. Discrete & Continuous Dynamical Systems, 2005, 13 (2) : 361-383. doi: 10.3934/dcds.2005.13.361
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