Differential and Integral Equations

Stationary solutions of a singular Navier-Stokes enthalpy-heat conduction system

José L. Boldrini, Sebastián Lorca P., and Herme Soto

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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.

Article information

Differential Integral Equations, Volume 27, Number 5/6 (2014), 511-530.

First available in Project Euclid: 3 April 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems 76D99: None of the above, but in this section 76R99: None of the above, but in this section 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Boldrini, José L.; Lorca P., Sebastián; Soto, Herme. Stationary solutions of a singular Navier-Stokes enthalpy-heat conduction system. Differential Integral Equations 27 (2014), no. 5/6, 511--530. https://projecteuclid.org/euclid.die/1396558095

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