An Improved Bilinear Estimate for Benjamin-ono Type Equations
نویسنده
چکیده
A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem ut − |D| αux + uux = 0 in (−T, T ) × R u(0) = u0 is proved, for 1 < α < 2. As a consequence, local well-posedness in H(R) ∩ Ḣ(R) 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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