A refinement of the Strichartz inequality on the saddle and applications

摘要

We consider the nonlinear nonelliptic Schrodinger equation defined by i partial derivative(t)u + (partial derivative(2)(x) - partial derivative(2)(y))u + gamma vertical bar u vertical bar(2)u =0 with initial datum in L-2(R-2). We show that if the solution blows up in finite time, then there is a mass concentration phenomenon near the blow-up time. The key ingredient is a refinement of the Strichartz inequality on the saddle. (C) 2006 Elsevier Inc. All rights reserved.