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arXiv · 1702.03191

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

Luc Molinet·Didier Pilod·Stéphane Vento
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Abstract

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

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Luc Molinet, Didier Pilod, Stéphane Vento. 2017-02-10. On well-posedness for some dispersive perturbations of Burgers' equation. https://arxiv.org/abs/1702.03191

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