Zero dissipation limit and stability of boundary layers for the heat conductive Boussinesq equations in a bounded domain. Issue 3 (3rd June 2015)

• Record Type: Journal Article
• Authors: Wang, Jing; Xie, Feng
• Is Part Of: Proceedings. Volume 145:Issue 3(2015)
• Page Start: 611
• Page End: 637
• Publication Date: 2015-06-03
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210513000875
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : In this paper, we study the zero dissipation limit of the initial boundary-value problem of the multi-dimensional Boussinesq equations with viscosity and heat conductivity. Such equations are used as models for the motion of multi-dimensional incompressible fluids in atmospheric and oceanographic turbulence. In particular, they describe the thermal convection of an incompressible flow, and constitute the relations between the velocity field, the pressure and the local temperature. Under the Navier slip boundary condition in the velocity field and the thermal isolation boundary condition for the temperature, we prove the existence of weak amplitude characteristic boundary layers. Then, by a standard energy method, we prove the L 2 convergence of the solutions when both the viscosity and the heat conductivity coefficients tend to 0.