Global Weak Solutions to the Navier-Stokes-Darcy-Boussinesq System for Thermal Convection in Coupled Free and Porous Media Flows
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914916846272512 |
|---|---|
| author | Wang, Xiaoming Wu, Hao |
| author_facet | Wang, Xiaoming Wu, Hao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_11243 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Global Weak Solutions to the Navier-Stokes-Darcy-Boussinesq System for Thermal Convection in Coupled Free and Porous Media Flows Wang, Xiaoming Wu, Hao Analysis of PDEs 35D30, 35K61, 76D03, 76D05, 76S05 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. |
| title | Global Weak Solutions to the Navier-Stokes-Darcy-Boussinesq System for Thermal Convection in Coupled Free and Porous Media Flows |
| topic | Analysis of PDEs 35D30, 35K61, 76D03, 76D05, 76S05 |
| url | https://arxiv.org/abs/2011.11243 |