Blowup for the nonlinear Schr\"odinger equation with an inhomogeneous   damping term in the $L^2$ critical case
  We consider the nonlinear Schr\"odinger equation with $L^2$-critical exponent and an inhomogeneous damping term. By using the tools developed by Merle and Raphael, we prove the existence of blowup phenomena in the energy space $H^1(\mathbb{R})$. 
Sim\~ao Correia
math.AP