On the local well-posedness for the nonlinear Schrodinger equation with spatial variable coefficient

We study a new type of nonlinear Schrodinger equation where the coefficient of Laplacian depends on spatial variable. Based on a modified Hankel transform and delicate frequency estimates, we establish the local well-posedness of the NLS with spatial variable coefficient in the weighted Lebesgue space for n >= 2, and extend the Strichartz estimates to the non-radially Schrodinger equation with spatial variable coefficient in 2D Euclidian space. (C) 2016 Elsevier Inc. All rights reserved.