On well-posedness for some dispersive perturbations of Burgers' equation

2017/02/10 by Molinet, Luc, Pilod, Didier, Vento, Stéphane · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.03191

Abstract

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(u²), 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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