Global Well-Posedness of an Initial-Boundary Value Problem of the 2-D Incompressible Navier-Stokes-Darcy System

Liu, Pan; Liu, Wenjuan

doi:10.1007/s10440-018-0197-7

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2020

2024

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Cited by 5 publications

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“…[16,22,27,32,33,37] and the references therein). We refer to [30] for an attempt on the Navier-Stokes-Darcy system for isothermal incompressible flows in a two-dimensional strip domain.…”

Section: Introductionmentioning

confidence: 99%

Global Weak Solutions to the Navier-Stokes-Darcy-Boussinesq System for Thermal Convection in Coupled Free and Porous Media Flows

Wang¹,

Wu²

2020

Preprint

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We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of global weak solutions to the initial boundary value problem subject to the Lions and Beavers-Joseph-Saffman-Jones interface conditions. The proof is based on a proper time-implicit discretization scheme combined with the Leray-Schauder principle and compactness arguments. Next, we establish a weak-strong uniqueness result such that a weak solution coincides with a strong solution emanating from the same initial data as long as the latter exists.

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“…[16,22,27,32,33,37] and the references therein). We refer to [30] for an attempt on the Navier-Stokes-Darcy system for isothermal incompressible flows in a two-dimensional strip domain.…”

Section: Introductionmentioning

confidence: 99%