Abstract
We prove the global well-posedness of the two-dimensional Boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data [u0∈L2, curlu0∈L∞ and θ0∈Bq,p2−2/p with p∈(1,∞), q∈(2,∞)]. Our method is based on the maximal regularity for heat equation.
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