Inviscid limit for the viscous 2D Boussinesq system with temperature-dependent diffusivity

2021/01/18 by Mohamed Zerguine, Zerguine, Mohamed, Youssouf Maafa +1
Economics, Econometrics and Finance · Engineering · Mathematics · #35B33 #35Q35 #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2101.07014

openalex publication_date 2021/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish global-posedness in time for the viscous Boussinesq equations in two dimensions of space with temperature-dependent diffusivity in the framework of a smooth vortex patch. We also provide the inviscid limit for velocity, temperature, and associated flow toward the system studied very recently in \citePaicu-Zhu as soon as the viscosity goes to zero, and quantify the rate of convergence.

Related

• Global Well-posedness for The 2D Boussinesq System Without Heat Diffusion and With Either Anisotropic Viscosity or Inviscid Voigt-α Regularization
• Growth of curvature and perimeter of temperature patches in the 2D Boussinesq equations
• Global well-posedness for 2-D Boussinesq system with the temperature-dependent viscosity and supercritical dissipation
• Global regularity of non-diffusive temperature fronts for the 2D viscous Boussinesq system
• Blowup in Stagnation-point Form Solutions of the Inviscid 2d Boussinesq Equations