2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225832A 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.Analysis of PDEs35Q53 (Primary); 35B30, 35S10, 76B15 (Secondary)text