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Titi, Jinkai Li","submitted_at":"2015-02-22T05:32:24Z","abstract_excerpt":"We prove the global well-posedness of the two-dimensional Boussinesq equations with only vertical dissipation. The initial data $(u_0,\\theta_0)$ are required to be only in the space $X=\\{f\\in L^2(\\mathbb R^2)\\,|\\,\\partial_xf\\in L^2(\\mathbb R^2)\\}$, and thus our result generalizes that in [C. Cao, J. Wu, Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation, Arch. Rational Mech. Anal., Vol. 208 (2013), 985-1004], where the initial data are assumed to be in $H^2(\\mathbb R^2)$. 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