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Global-in-time strong solvability of the multi-dimensional one-phase Stefan problem for an incompressible viscous fluid

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Abstract

In the present paper, we consider the multi-dimensional one-phase Stefan problem describing the process of phase transition in an incompressible viscous fluid. The model is described as a free boundary problem consisting of the heat equation with a transport term and the Navier–Stokes equations. We prove the existence of a global-in-time strong solution with small data by introducing Lagrangian coordinates.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering, Tamagawa University, 6-1-1 Tamagawa-Gakuen, 194-8610, Machida, Tokyo, Japan

    Yoshiaki Kusaka

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  1. Yoshiaki Kusaka
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Correspondence to Yoshiaki Kusaka.

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Kusaka, Y. Global-in-time strong solvability of the multi-dimensional one-phase Stefan problem for an incompressible viscous fluid. Japan J. Indust. Appl. Math. 30, 415–439 (2013). https://doi.org/10.1007/s13160-013-0108-2

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  • DOI: https://doi.org/10.1007/s13160-013-0108-2

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