H2 Blowup Result For A Schrodinger Equation With Nonlinear Source Term

Abstract

In this paper, we consider the nonlinear Schrodinger equation on ℝN, N ≥ 1, (fomula presented), with H2 -subcritical nonlinearities: α > 0, (N − 4)α < 4 and Reλ > 0. For any given compact set K⊂ℝN, we construct H2 solutions that are defined on (−T, 0) for some T > 0, and blow up exactly on K at t = 0. We generalize the range of the power α in the result of Cazenave, Han and Martel [5]. The proof is based on the energy estimates and compactness arguments