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

  • Stéphane Vento

    Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 99, avenue Jean-Baptiste Clément, F-93 430 Villetaneuse, France
  • Luc Molinet

    Institut Denis Poisson, Université de Tours, Université d'Orléans, CNRS (UMR 7013), Parc Grandmont, 37200 Tours, France
  • Didier Pilod

    Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP: 21945-970, Rio de Janeiro, RJ, Brazil

Abstract

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. 1719–1756

DOI 10.1016/J.ANIHPC.2017.12.004