Global regularity for a coupled Cahn-Hilliard-Boussinesq system on bounded domains

Zhao, Kun

doi:10.1090/s0033-569x-2011-01241-5

Cited by 7 publications

(8 citation statements)

References 32 publications

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“…Problems like and (1.4) and (1.5) have been considered in the literature, as far as we know, for regular potentials only. Problem (1.5) in the inviscid case has been analyzed in [52,53] in a two-dimensional bounded domain. The first contribution contains global existence and uniqueness of smooth solutions with smooth initial data.…”

Section: Introductionmentioning

confidence: 99%

The Cahn-Hilliard-Boussinesq system with singular potential

Grasselli

Poiatti

2022

Communications in Mathematical Sciences

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We consider a Cahn-Hilliard-Boussinesq system with positive heat diffusivity and singular potential on a two-dimensional bounded domain with suitable boundary conditions. For the corresponding initial and boundary value problem we prove the existence of strong solutions and the well-posedness for weak solutions. Then we set the diffusivity equal to zero. In this case, the model can be viewed as an approximation of the two-dimensional compressible Navier-Stokes-Cahn-Hilliard system proposed in [

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Section: Introductionmentioning

confidence: 99%

The Cahn-Hilliard-Boussinesq system with singular potential

Grasselli

Poiatti

2022

Communications in Mathematical Sciences

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“…Recently, the couplings of the Cahn-Hilliard equation with other basic modeling equations also have been proposed in various situation to describe complicated phenomena in fluid mechanics involving phase transition, such as the Cahn-Hilliard-Navier-Stokes (CHNS) equation [5,9,13,14,19], the Cahn-Hilliard-Hele-Shaw (CHHS) [4,12,[22][23][24] equation, and the Cahn-Hilliard-Boussinesq (CHB) [26] equation.…”

Section: Introductionmentioning

confidence: 99%

Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model

Cheng¹,

Feng²

2017

J. Nonlinear Sci. Appl.

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The global well-posedness analysis for the three dimensional dynamic Cahn-Hilliard-Stokes (CHS) model is provided in this paper. In this model, the velocity vector is determined by the phase variable by both the Darcy law and the Stokes equation. Based on the analysis of weak solutions to the CHS equation by the standard Galerkin method, we present a global in time strong solution for the CHS model. Moreover, the existence and the uniqueness of the strong solution are also proven.

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“…It would be interesting to include Marangoni effects in the model studied therein. At last, we also refer to [42] for the Cahn-Hilliard-Boussinesq equation with the specific assumption that λ and κ are positive constants and µ = 0.…”

Section: Introductionmentioning

confidence: 99%

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

2016

Eur. J. Appl. Math

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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.

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Global regularity for a coupled Cahn-Hilliard-Boussinesq system on bounded domains

Cited by 7 publications

References 32 publications

The Cahn-Hilliard-Boussinesq system with singular potential

The Cahn-Hilliard-Boussinesq system with singular potential

Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model

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

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