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Global regularity for the 2D Boussinesq equations with partial viscosity terms. (English) Zbl 1100.35084
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 {\it H. K. Moffatt} [R. L. Ricca (ed.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 3--10 (2001; Zbl 1100.76001)].

35Q35PDEs in connection with fluid mechanics
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
76D03Existence, uniqueness, and regularity theory
76D09Viscous-inviscid interaction
Full Text: DOI
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[11] Y. Taniuchi, A note on the blow-up criterion for the inviscid 2-D Boussinesq equations, in: R. Salvi (Ed.), The Navier-Stokes Equations: Theory and Numerical Methods, Lecture Notes in Pure and Applied Mathematics, vol. 223, 2002, pp. 131-140. · Zbl 0991.35070