1D quintic nonlinear Schrödinger equation with white noise dispersion

International audienceIn this article, we improve the Strichartz estimates obtained in [12] for the Schrödinger equation with white noise dispersion in one dimension. This allows us to prove global well posedness when a quintic critical nonlinearity is added to the equation. We finally show that the white noise dispersion is the limit of smooth random dispersion

Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method

Dedicated to the memory of Professor Jean GinibreIn this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy problem both on the real line and on the circle, we apply the short-time Fourier restriction method to establish a priori estimate for small and smooth solutions in Sobolev spaces H[s] with s > 1/4

Normal form and global solutions for the Klein-Gordon-Zakharov equations(Nonlinear Evolution Equations and Their Applications)

Available from British Library Document Supply Centre- DSC:DXN062667 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model

We consider the global evolution problem for a model which couples together a nonlinear wave equation and a nonlinear Klein-Gordon equation, and was independently introduced by LeFloch and Y. Ma and by Q. Wang. By revisiting the Hyperboloidal Foliation Method, we establish that a weighted energy of the solutions remains (almost) bounded for all times. The new ingredient in the proof is a hierarchy of fractional Morawetz energy estimates (for the wave component of the system) which is defined from two conformal transformations. The optimal case for these energy estimates corresponds to using the scaling vector field as a multiplier for the wave component.Comment: 19 page