4 papers
math.AP2026
On the well-posedness of the KP-I equation
Zihua Guo, Luc Molinet
We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in for and unconditional global well-posedn…
math.AP2025
Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation
Luc Molinet, Didier Pilod, Stéphane Vento
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…
math.AP2025
Refined bilinear Strichartz estimates with application to the well-posedness of periodic generalized KdV type equations
Luc Molinet, Tomoyuki Tanaka
We improve our previous result [L. Molinet and T. Tanaka, Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations, J. Funct. Anal. 283 (2022),…
math.AP2024
Self-similar solutions for the generalized fractional Korteweg-de Vries equation
Luc Molinet, Stéphane Vento, Fred Weissler
We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation with…