Axel Grünrock

LOW REGULARITY LOCAL WELL-POSEDNESS OF THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH PERIODIC INITIAL DATA

The Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition is considered. Local well-posedness for data

Bi- and trilinear Schrödinger estimates in one space dimension with applications to cubic NLS and DNLS

u_0

An improved local well-posedness result for the modified KdV equation

in the space

The Fourier restriction norm method for the Zakharov-Kuznetsov equation

widehat{H}^{s}_{r}(mathbb{T})

On the hierarchies of higher order mKdV and KdV equations

, defined by the norms

Local well-posedness for the modified KdV equation in almost critical

|u_0|_{widehat{H}^{s}_{r}(mathbb{T})} = |langlexirangle^swidehat{u}_0|_{ell^{r}_{xi}}

\widehat {H^r_s}

, is shown in the parameter range

-spaces

s ge frac{1}{2}

Global solutions for the Dirac-Klein-Gordon system in two space dimensions

,

On KP-II type equations on cylinders

2>r>frac{4}{3}