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An improved bilinear estimate for Benjamin-Ono type equations

S. Herr
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Abstract

A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem associated to u_t - |D|^αu_x + uu_x =0 is proved, for 1< α<2. As a consequence, local well-posedness in H^s(\R) \cap \dot{H}^{-ω}(\R) follows for s >-{3/4}(α-1) and ω=1/α-1/2. This extends to global well-posedness for all s \geq 0.

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S. Herr. 2005-09-09. An improved bilinear estimate for Benjamin-Ono type equations. https://arxiv.org/abs/math/0509218

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