an:05043542
Zbl 1100.35084
Chae, Dongho
Global regularity for the 2D Boussinesq equations with partial viscosity terms
EN
Adv. Math. 203, No. 2, 497-513 (2006).
00177106
2006
j
35Q35 76B03 76D03 76D09
Boussinesq equations; vanishing viscosity limit; vanishing diffusivity limit; global regularity
Summary: We prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity. We also prove that as diffusivity (viscosity) tends to zero, the solutions of the fully viscous equations converge strongly to those of zero diffusion (viscosity) equations. Our result for the zero diffusion system, in particular, solves the Problem no. 3 posed by \textit{H. K. Moffatt} [R. L. Ricca (ed.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 3--10 (2001; Zbl 1100.76001)].
Zbl 1100.76001