A refinement of the Strichartz inequality on the saddle and applications

We consider the nonlinear nonelliptic Schrödinger equation defined by i∂tu + (∂2 x − ∂2 y )u + γ |u|2u = 0 with initial datum in L2(R2). 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. © 2006 Elsevier Inc. All rights reserved.