# Analysis of a system modelling the motion of a piston in a viscous gas

Analysis of a system modelling the motion of a piston in a viscous gas We study a free boundary problem modelling the motion of a piston in a viscous gas. The gas-piston system fills a cylinder with fixed extremities, which possibly allow gas from the exterior to penetrate inside the cylinder. The gas is modeled by the 1D compressible Navier–Stokes system and the piston motion is described by the second Newton’s law. We prove the existence and uniqueness of global in time strong solutions. The main novelty brought in by our results is that they include the case of nonhomogeneous boundary conditions which, as far as we know, have not been studied in this context. Moreover, even for homogeneous boundary conditions, our results require less regularity of the initial data than those obtained in previous works. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

# Analysis of a system modelling the motion of a piston in a viscous gas

, Volume 19 (3) – Sep 30, 2016
29 pages

/lp/springer_journal/analysis-of-a-system-modelling-the-motion-of-a-piston-in-a-viscous-gas-p2u0FiRiz8
Publisher
Springer International Publishing
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-016-0293-2
Publisher site
See Article on Publisher Site

### Abstract

We study a free boundary problem modelling the motion of a piston in a viscous gas. The gas-piston system fills a cylinder with fixed extremities, which possibly allow gas from the exterior to penetrate inside the cylinder. The gas is modeled by the 1D compressible Navier–Stokes system and the piston motion is described by the second Newton’s law. We prove the existence and uniqueness of global in time strong solutions. The main novelty brought in by our results is that they include the case of nonhomogeneous boundary conditions which, as far as we know, have not been studied in this context. Moreover, even for homogeneous boundary conditions, our results require less regularity of the initial data than those obtained in previous works.

### Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Sep 30, 2016

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