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Global well-posedness of incompressible Bénard problem with zero dissipation or zero thermal diffusivity. (English) Zbl 1426.35193
Summary: In this paper, we establish the global well-posedness of the classical solution for the two-dimensional Bénard problem with zero dissipation or zero thermal diffusivity. Our work is partially motivated by the results about Boussinesq equations with zero dissipation or zero thermal diffusivity in [D. Chae, Adv. Math. 203, No. 2, 497–513 (2006; Zbl 1100.35084)] and [T. Y. Hou and C. Li, Discrete Contin. Dyn. Syst. 12, No. 1, 1–12 (2005; Zbl 1274.76185)].

MSC:
35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B65 Smoothness and regularity of solutions to PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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