May/June 2014 Stationary solutions of a singular Navier-Stokes enthalpy-heat conduction system
José L. Boldrini, Sebastián Lorca P., Herme Soto
Differential Integral Equations 27(5/6): 511-530 (May/June 2014). DOI: 10.57262/die/1396558095


We present a result on existence of stationary solutions of a system coupling singular Navier-Stokes equations to a enthalpy-heat equation. This system may model the solidification process of certain classes of materials by taking into consideration the possibility of flow in the melt; thus, the singular Navier-Stokes equations only holds in the a priori unknown molten region and one has a free-boundary value problem to be solved. To obtain solutions for such system, we initially consider a sequence of approximate problems associated to an appropriate regularizations of the original one, which are obtained by a suitable modification such that the approximate equations for the flow hold in the entire domain. After analyzing these approximate problems, by using compactness arguments, we take limits to obtain generalized solutions of the original problem.


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José L. Boldrini. Sebastián Lorca P.. Herme Soto. "Stationary solutions of a singular Navier-Stokes enthalpy-heat conduction system." Differential Integral Equations 27 (5/6) 511 - 530, May/June 2014.


Published: May/June 2014
First available in Project Euclid: 3 April 2014

zbMATH: 1340.35398
MathSciNet: MR3273583
Digital Object Identifier: 10.57262/die/1396558095

Primary: 35R35 , 76D99 , 76R99 , 80A22

Rights: Copyright © 2014 Khayyam Publishing, Inc.


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Vol.27 • No. 5/6 • May/June 2014
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