13 citations · 13 across the 3 of their papers we have counts for
5 papers
Bi- and trilinear Schroedinger estimates in one space dimension with applications to cubic NLS and DNLS
Axel Gruenrock
The Fourier transforms of the products of two respectively three solutions of the free Schroedinger equation in one space dimension are estimated in mixed and, in the first case we…
Bounds in time for the Klein-Gordon-Schroedinger and the Zakharov system
Axel Gruenrock, Hartmut Pecher
It is shown that the spatial Sobolev norms of regular global solutions of the (2+1),(3+1) and (4+1)-dimensional Klein-Gordon-Schroedinger system and the (2+1) and (3+1)-dimensional…
An improved local wellposedness result for the modified KdV equation
Axel Gruenrock
The Cauchy problem for the modified KdV equation is shown to be locally well posed for data u_0 in the space \hat(H^r_s) defined by the norm ||u_0||:=||<ξ>^s \hat(u_0)||_L^r', prov…
Some local wellposedness results for nonlinear Schroedinger equations below L^2
Axel Gruenrock
We prove some local (in time) wellposedness results for nonlinear Schroedinger equations with rough data, that is, the initial value belongs to some Sobolev space of negative index…
On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations
Axel Gruenrock
The Cauchy- and periodic boundary value problem for the nonlinear Schroedinger equations in space dimensions [u_t - iΔu = (\nabla \bar{u})^β, |β|=m \ge 2, u(0)=u_0 \in H^{s+1}_…