Didier Pilod

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math.AP2026

Continuum of finite point blowup rates for the critical generalized Korteweg-de Vries equation

Yvan Martel, Didier Pilod

For any $I^½ \in (\frac{3}{7}, \frac{1}{2})$ , we prove the existence of an $H^{1}$ solution $u$ of the mass critical generalized Korteweg-de Vries equation on the time interval $(0, T_{0}]$ , for s…

math.AP2025

Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation

We consider the Cauchy problem associated to a class of dispersive perturbations of Burgers' equations, which contains the low dispersion Benjamin-Ono equation, (also known as low…