We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin–Ono equation
is locally well-posed in when . As a consequence, we obtain global well-posedness in the energy space as soon as , i.e. .
Cite this article
Stéphane Vento, Luc Molinet, Didier Pilod, On well-posedness for some dispersive perturbations of Burgers' equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, pp. 1719–1756DOI 10.1016/J.ANIHPC.2017.12.004