https://hal.inria.fr/hal-00848075Colin, ThierryThierryColinCMLA - Centre de Mathématiques et de Leurs Applications - ENS Cachan - École normale supérieure - Cachan - CNRS - Centre National de la Recherche ScientifiqueOn a nonlocal, nonlinear Schrödinger equation occuring in Plasma PhysicsHAL CCSD1993[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Colin, ThierryV. Makhankov, I. Puzynin and O. Pashaev2013-07-25 13:41:362021-04-15 03:31:542013-07-25 14:11:15enConference papersapplication/pdf1In this work, our goal is to study the Cauchy problem for a nonlocal, nonlinear Schr ̈odinger equation occuring in Plasma Physics. We shall construct solutions in the energy space; we give some sufficient conditions on the initial data which ensure that the solutions are global and we show that in some cases, finite time blow up occurs. We prove the existence of standing waves, solution to these equations and provide some stability results.