A multidimensional piston problem for the Euler equations for compressible flow
Shuxing Chen - School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China (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.
Received: May 2004; Revised: March 2005; Published: April 2005.
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