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Global weak solutions for a model of two-phase flow with a single interface

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Abstract

We consider a simple nonlinear hyperbolic system modeling the flow of an inviscid fluid. The model includes as state variable the mass density fraction of the vapor in the fluid, and then, phase transitions can be taken into consideration; moreover, phase interfaces are contact discontinuities for the system. We focus on the special case of initial data consisting of two different phases separated by an interface. We find explicit bounds on the (possibly large) initial data in order that weak entropic solutions exist for all times. The proof exploits a carefully tailored version of the front-tracking scheme.

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Authors and Affiliations

  1. Department of Engineering and Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Debora Amadori

  2. Department of Mathematics and Computer Science, University of Udine, Udine, Italy

    Paolo Baiti & Edda Dal Santo

  3. Department of Mathematics and Computer Science, University of Ferrara, Ferrara, Italy

    Andrea Corli

Authors
  1. Debora Amadori
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  2. Paolo Baiti
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  3. Andrea Corli
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  4. Edda Dal Santo
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Correspondence to Andrea Corli.

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Amadori, D., Baiti, P., Corli, A. et al. Global weak solutions for a model of two-phase flow with a single interface. J. Evol. Equ. 15, 699–726 (2015). https://doi.org/10.1007/s00028-015-0278-2

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  • DOI: https://doi.org/10.1007/s00028-015-0278-2

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