A multidimensional piston problem for the Euler equations for compressible flow

Shuxing Chen; Gui-Qiang Chen; Zejun Wang; Dehua Wang

doi:10.3934/dcds.2005.13.361

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2005, Volume 13, Issue 2: 361-383. Doi: 10.3934/dcds.2005.13.361

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A multidimensional piston problem for the Euler equations for compressible flow

1.
School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433
2.
Institute of Mathematics, Fudan University, Shanghai 200433
3.
Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240
4.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received: April 30, 2004

Revised: February 28, 2005

Published: January 2005

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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.

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Mathematics Subject Classification: 35L65, 76N10.

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