In this talk we consider inhomogeneous cubic-quintic NLS in space dimension d=3 :
We discuss local well-posedness, finite time blowup, and small data scattering and non-scattering for the ICQNLS when K1,K2inC(mathbbR3)capC4(mathbbR3setminus0) satisfy growth condition |partialjKi(x)|lesssim|x|bij(j=0,1,2,3) for some bi>0 and for xneq0 . To this end we use the Sobolev inequality for the functions finH1 such that |mathbfLf|H1<infty , where mathbfL is the angular momentum operator defined by mathbfL=xtimes(inabla) .