Global existence of weak solutions for a viscous two-phase model |
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Authors: | Steinar Evje Kenneth H Karlsen |
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Institution: | a International Research Institute of Stavanger (IRIS), Prof. Olav Hanssensvei 15, NO-4068 Stavanger, Norway b Centre of Mathematics for Applications (CMA), University of Oslo, PO Box 1053, Blindern, N-0316 Oslo, Norway |
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Abstract: | The purpose of this paper is to explore a viscous two-phase liquid-gas model relevant for well and pipe flow. Our approach relies on applying suitable modifications of techniques previously used for studying the single-phase isothermal Navier-Stokes equations. A main issue is the introduction of a novel two-phase variant of the potential energy function needed for obtaining fundamental a priori estimates. We derive an existence result for weak solutions in a setting where transition to single-phase flow is guaranteed not to occur when the initial state is a true mixture of both phases. Some numerical examples are also included in order to demonstrate characteristic behavior of solutions. In particular, we illustrate how two-phase flow is genuinely different compared to single-phase flow concerning the behavior of an initial mass discontinuity. |
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Keywords: | 76T10 76N10 65M12 35L65 |
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