PDE Seminar (2019/1/11): Well-posedness for a system of quadratic derivative nonlinear Schr\”odinger equations with radial initial data

2019-1-11 16:30 - 2019-1-11 18:00
Faculty of Science Building #3, Room 309
Hiroyuki Hirayama (University of Miyazaki)
We consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations. This system was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. The well-posedness of this system in the Sobolev space was obtained in our previous works (H (2014), H and S. Kinoshita (2019)). In this talk, we improve these results for conditional radial initial data by rewriting the system into radial form. This talk is based on a joint work with Shinya Kinoshita and Mamoru Okamoto.