On well-posedness for some dispersive perturbations of Burgers' equation
Résumé
We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin-Ono equation
∂_t u − D^α_x ∂_x u = ∂_x(u^2) , 0 < α ≤ 1, is locally well-posed in H^s (R) when s > 3 /2 − 5α /4. As a consequence, we obtain global well-posedness in the energy space H^{α/2} (R) as soon as α > 6/7 .
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