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

Debayan Maity (1) , Takéo Takahashi (2, 3) , Marius Tucsnak (4)

1 TIFR-CAM - Center for Applicable Mathematics [Bangalore]
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 IECL - Institut Élie Cartan de Lorraine
4 IMB - Institut de Mathématiques de Bordeaux

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 on 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.

Mots clés: fluid-particle interaction; Compressible Navier-Stokes System

Domaines: Equations aux dérivées partielles [math.AP]

Debayan Maity, Takéo Takahashi, Marius Tucsnak. Analysis of a system modelling the motion of a piston in a viscous gas. Journal of Mathematical Fluid Mechanics, 2017, 19 (3), pp.551-579. ⟨10.1007/s00021-016-0293-2⟩. ⟨hal-01285089⟩