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A Mathematical analysis of fluid motion in irreversible phase transitions

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Abstract

This article addresses the mathematical analysis of a model for the irreversible solidification process of certain materials by taking in consideration the effects of natural convection in molten regions. Such a model consists of a highly nonlinear system of partial differential equations coupled to a doubly nonlinear differential inclusion. The existence of weak–strong solutions for the system is proved, and certain mathematical effects of advection on the regularity of the solutions are discussed.

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Authors and Affiliations

  1. Departamento de Matemática Instituto de Matemática Estatística e Computação Científica, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda, 651, Campinas, SP, 13083-859, Brazil

    José Luiz Boldrini & Gabriela Planas

  2. Departamento de Matemática, Universidade de Brasília, Asa Norte, Brasília, DF, 70910-900, Brazil

    Luís H. de Miranda

Authors
  1. José Luiz Boldrini
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  2. Luís H. de Miranda
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  3. Gabriela Planas
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Correspondence to Gabriela Planas.

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Boldrini, J.L., de Miranda, L.H. & Planas, G. A Mathematical analysis of fluid motion in irreversible phase transitions. Z. Angew. Math. Phys. 66, 785–817 (2015). https://doi.org/10.1007/s00033-014-0434-5

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  • DOI: https://doi.org/10.1007/s00033-014-0434-5

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