Francis Ribaud

Well-posedness results for the generalized Benjamin-Ono equation with arbitrary large initial data

We prove new local well-posedness results for the generalized Benjamin-Ono equation (GBO) ∂tu+ℋ∂x2u+uk∂xu=0, k ≥ 2. By combining a gauge transformation with dispersive estimates, we establish the local well-posedness of GBO in H s (ℝ) for s ≥ 1/2 if k ≥ 5, s > 1/2 if k=2,4, and s≥ 3/4 if k=3. Moreover, we prove that in all these cases, the flow map is locally Lipschitz on H s (ℝ).

On the Cauchy Problem for the Generalized Korteweg-de Vries Equation

Abstract We consider the local and global Cauchy problem for the generalized Korteweg-de Vries equation , with initial data in homogeneous and nonhomogeneous Besov spaces. This allows us to slightly extend known results on this problem. Furthermore we prove existence and uniqueness of self-similar solutions.

Well-Posedness Results for the Three-Dimensional Zakharov--Kuznetsov Equation

We prove the local well-posedness of the three-dimensional Zakharov--Kuznetsov equation

The Global Cauchy Problem in Bourgain's-Type Spaces for a Dispersive Dissipative Semilinear Equation

\partial_tu+\Delta\partial_xu+ u\partial_xu=0

Regular and self-similar solutions of nonlinear Schrödinger equations

in the Sobolev spaces

On the Flow Map for a Class of Parabolic Equations

H^s(\mathbb{R}^3)

On the low regularity of the Korteweg-de Vries-Burgers equation

,

Well-posedness results for the generalized Benjamin–Ono equation with small initial data

s>1

The cauchy problem for dissipative Korteweg de Vries equations in Sobolev spaces of negative order

, as well as in the Besov space

Global solutions and self-similar solutions of semilinear wave equation

B^{1,1}_2(\mathbb{R}^3)