20 citations · 76 across the 11 of their papers we have counts for
11 papers
On the generalized Zakharov-Kuznetsov equation at critical regularity
Axel Gruenrock
The Cauchy problem for the generalized Zakharov-Kuznetsov equation is considered in space dimensions …
On the wave equation with quadratic nonlinearities in three space dimensions
Axel Gruenrock
The Cauchy problem for the nonlinear wave equation in three space dimensions is considered. The data are assumed…
On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations
Axel Gruenrock
The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation is shown to be locally well-posed in al…
Global solutions for the Dirac-Klein-Gordon system in two space dimensions
Axel Gruenrock, Hartmut Pecher
The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In…
A remark on global well-posedness below L^2 for the gKdV-3 equation
Axel Gruenrock, Mahendra Panthee, Jorge Drumond Silva
The I-method in its first version as developed by Colliander et al. is applied to prove that the Cauchy-problem for the generalised Korteweg-de Vries equation of order three (gKdV-…
Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces
Axel Gruenrock, Luis Vega
We study the Cauchy problem for the modified KdV equation for data u_0 in the space ^H^r_s defined by the norm ||u_0||_{^H^r_s}:=||<ξ>^s u^_0||_{L^r'_ξ}. Local well-posedness of th…