报告地点：行健楼学术活动室665
邀请人：网赌
摘要：We consider the kinetic derivative NLS, which is a 1D nonlinear Schrodinger equation with a non-local cubic derivative nonlinear term. The equation has dissipative (resp. anti-dissipative) nature when the coefficient of the non-local term is negative (resp. positive). It was proved by the speaker and Tsutsumi that the initial value problem on the real line is locally well-posed in Sobolev space H^s with s>1 in the dissipative case. In this talk, we first show local well-posedness in H^2 in the anti-dissipative case by the energy method combined with a suitable gauge transformation. We next focus on the dissipative case and derive a global-in-time a priori bound in H^2, which implies global well-posedness in H^2. If time permits, we also report on recent progress regarding asymptotic behavior of small solutions in both dissipative and anti-dissipative cases. This talk is based on joint work with Kiyeon Lee (KAIST).
