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Especially we consider two types of nonlocal operators:\n  $\\mathcal{N}=\\mathcal{H}$, the Hilbert transform,\n  $\\mathcal{N}=(1-\\partial_{xx} )^{-\\alpha}$.\n  In this paper, we show several global existence of weak solutions depending on the range of $\\gamma$ and $\\delta$. 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Especially we consider two types of nonlocal operators:\n  $\\mathcal{N}=\\mathcal{H}$, the Hilbert transform,\n  $\\mathcal{N}=(1-\\partial_{xx} )^{-\\alpha}$.\n  In this paper, we show several global existence of weak solutions depending on the range of $\\gamma$ and $\\delta$. 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