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

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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.

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Authors and Affiliations

  1. Institut de Mathématiques, Université de Bordeaux, Bordeaux INP, CNRS, 33400, Talence, France

    Debayan Maity & Marius Tucsnak

  2. INRIA Nancy-Grand Est, 615, rue du Jardin Botanique, 54600, Villers-lès-Nancy, France

    Takéo Takahashi

Authors
  1. Debayan Maity
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  2. Takéo Takahashi
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  3. Marius Tucsnak
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Correspondence to Marius Tucsnak.

Additional information

The first author is member of an IFCAM-project, Indo-French Center for Applied Mathematics—UMI IFCAM, Bangalore, India, supported by DST–IISc–CNRS—and Université Paul Sabatier Toulouse III. The research of the first author was supported by the Airbus Group Corporate Foundation Chair in Mathematics of Complex Systems established in TIFR, Bangalore.

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Maity, D., Takahashi, T. & Tucsnak, M. Analysis of a system modelling the motion of a piston in a viscous gas. J. Math. Fluid Mech. 19, 551–579 (2017). https://doi.org/10.1007/s00021-016-0293-2

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