An improved bilinear estimate for Benjamin-Ono type equations
Abstract
A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem associated to ut - |D|αux + uux =0 is proved, for 1< α <2. As a consequence, local well-posedness in Hs() H-ω() follows for s >-3/4(α-1) and ω=1/α-1/2. This extends to global well-posedness for all s ≥ 0.
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