Global wellposedness of the modified Benjamin-Ono equation with initial data in H1/2

Perturbation theory for the Benjamin–Ono equation

We develop a perturbation theory for the Benjamin–Ono (BO) equation. This perturbation theory is based on the inverse scattering transform for the BO equation, which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. We find the expressions for the variations of the scattering data with respect to the potential, as well as the dual expression for the variat...

Benjamin-Ono Equation on a Half-Line

Global Wellposedness for a Modified Critical Dissipative Quasi-Geostrophic Equation

In this paper we study the following modified quasi-geostrophic equation ∂tθ + u · ∇θ + ν|D| θ = 0, u = |D|Rθ with ν > 0 and 0 < α < 1. This equation was firstly introduced by Constantin-Iyer-Wu in [10]. Here, we firstly prove the local existence result of smooth solutions by using the classical method, and then through constructing a suitable modulus of continuity we rule out all the possible ...

Global well-posedness in the Energy space for the Benjamin-Ono equation on the circle

We prove that the Benjamin-Ono equation is well-posed in H(T). This leads to a global well-posedeness result in H(T) thanks to the energy conservation. Résumé. Nous montrons que l’équation de Benjamin-Ono est bien posée dans H(T). Il découle alors de la conservation de l’énergie que la solution existe pour tout temps dans cette espace.

Global Wellposedness for a Modified Critical Dissipative Quasi-Geostropic Equation

In this paper we study the following modified quasi-geostrophic equation ∂tθ + u · ∇θ + ν|D| θ = 0, u = |D|Rθ with ν > 0 and 0 < α < 1. This equation was firstly introduced by Constantin-Iyer-Wu in [10]. Here, we first prove the local existence result of smooth solutions by using the energy method and the regularization effect of the transport equation with fractional diffusion, and then throug...