Open AccessA multidimensional piston problem for the Euler equations for compressible flow
Author(s) -
Shuxing Chen,
Gui–Qiang Chen,
Zejun Wang,
Dehua Wang
Publication year - 2005
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2005.13.361
Subject(s) - euler equations , piston (optics) , compressibility , compressible flow , euler's formula , isentropic process , expansive , flow (mathematics) , mathematics , mathematical analysis , physics , mechanics , thermodynamics , compressive strength , wavefront , optics
A multidimensional piston problem for the Euler equations for compressible isentropic flow is analyzed. The piston initially locates at the origin and experiences compressive and expansive motions with spherical symmetry. The initial singularity at the origin is one of the difficulties for this spherically symmetric piston problem. A local shock front solution for the compressive motion is constructed based on the linearization at an approximate solution and the Newton iteration. A global entropy solution for the piston problem is constructed by using a shock capturing approach and the method of compensated compactness