An improved bilinear estimate for Benjamin-Ono type equations
Abstract
Description
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.