Abstract
This paper is devoted to the well-posedness for dissipative KdV equations ut + uxxx + |Dx|2αu + uux = 0, 0 < α ≤ 1. An optimal bilinear estimate is obtained in Bourgain's type spaces, which provides global well-posedness in Hs(R), s > -3/4 for α ≤ 1/2 and s > -3/(5-2α) for α > 1/2.
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