Minimal-mass blow-up solutions for nonlinear Schrodinger equations with an inverse potential

We consider the following nonlinear Schrodinger equation with an inverse potential: i partial derivative u/partial derivative t + Delta u + vertical bar u vertical bar(d/N) u +/- 1/vertical bar x vertical bar(2 sigma) u = 0 in R-N. From the classical argument, the solution with subcritical mass (parallel to u parallel to(2) < parallel to Q parallel to(2)) is global and bounded in H-1(R-N). Here, Q is the ground state of the mass critical problem. Therefore, we are interested in the existence and behaviour of blow-up solutions for the threshold (parallel to u(0)parallel to(2) = parallel to Q parallel to(2)). Previous studies investigate the existence and behaviour of the critical-mass blow-up solution when the potential is smooth or unbounded but algebraically tractable. There exist no results when classical methods cannot be used, such as the inverse power type potential. However, in this paper, we construct a critical-mass finite-time blow-up solution. Moreover, we show that the blow-up solution converges to a certain blow-up profile in the virial space. (C) 2021 Elsevier Ltd. All rights reserved.