Blowup criteria for the focusing inhomogeneous nonlinear Schrödinger equation

In this talk I will discuss the blowup criteria for the focusing inhomogeneous nonlinear Schrödinger equation (INLS). Using the sharp Gagliardo-Nirenberg inequality together with localized virial estimates, we establish the blowup criteria for the focusing (INLS) in the mass-critical and energy-subcritical cases. These results extend well-known results of Ogawa-Tsutsumi (JDE 92, PAMS 111) for (NLS) to (INLS).