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Well-posedness of a diffuse-interface model for two-phase incompressible flows with thermo-induced Marangoni effect

Published online by Cambridge University Press:  25 July 2016

HAO WU
HAO WU*
Affiliation:
School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, 200433 Shanghai, China email: haowufd@yahoo.com
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Abstract

We investigate a non-isothermal diffuse-interface model that describes the dynamics of two-phase incompressible flows with thermo-induced Marangoni effect. The governing PDE system consists of the Navier--Stokes equations coupled with convective phase-field and energy transport equations, in which the surface tension, fluid viscosity and thermal diffusivity are allowed to be temperature dependent functions. First, we establish the existence and uniqueness of local strong solutions when the spatial dimension is two and three. Then, in the two-dimensional case, assuming that the L∞-norm of the initial temperature is suitably bounded with respect to the coefficients of the system, we prove the existence of global weak solutions as well as the existence and uniqueness of global strong solutions.

Keywords

35A0135A0235K2035Q35
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 3 , June 2017 , pp. 380 - 434
Copyright
Copyright © Cambridge University Press 2016 

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