110 citations · 432 across the 36 of their papers we have counts for
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Sharp ill-posedness result for the periodic Benjamin-Ono equation
Luc Molinet
We prove the discontinuity for the weak $ L^2(\T) $-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in $ H…
On ill-posedness for the one-dimensional periodic cubic Schrodinger equation
Luc Molinet
We prove the ill-posedness in $ H^s(\T) $, , of the periodic cubic Schrödinger equation in the sense that the flow-map is not continuous from $H^s(\T) $ into itself for any fi…
Global attractor and asymptotic smoothing effects for the weakly damped cubic Schrödinger equation in $L^2(\T)$
Luc Molinet
We prove that the weakly damped cubic Schrödinger flow in $L^2(\T)$ provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior…
Stability of multipeakons
Khaled El Dika, Luc Molinet
The Camassa-Holm equation possesses well-known peaked solitary waves that are called peakons. Their orbital stability has been established by Constantin and Strauss (2000). We prov…
Newtonian limit for weakly viscoelastic fluid flows of Olroyds' type
Luc Molinet, Raafat Talhouk
This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for…