Lp theory for Boussinesq system with Dirichlet boundary conditions. Issue 1 (25th January 2019)

• Record Type: Journal Article
• Authors: Acevedo, Paul; Amrouche, Chérif; Conca, Carlos
• Is Part Of: Applicable analysis. Volume 98:Issue 1/2(2019)
• Page Start: 272
• Page End: 294
• Publication Date: 2019-01-25
• Subjects: Grigory Panasenko; Boussinesq system -- non-homogeneous Dirichlet boundary conditions -- weak solution -- strong solution -- very weak solution; 35Q30 -- 49N60 -- 76D03; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1530762
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider the stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domainΩ ⊂ R 3 of classC 1, 1 with a possibly disconnected boundary. We prove the existence of weak solutions inW 1, p ( Ω ), strong solutions inW 2, p ( Ω ) and very weak solutions inL p ( Ω ) of the stationary Boussinesq system by assuming that the fluxes of the velocity are sufficiently small. Finally, as it is expected, we obtain the uniqueness of the solution by considering small data.