ON UNIQUENESS AND CONTINUATION PROPERTIES AFTER BLOW-UP TIME OF SELF-SIMILAR SOLUTIONS OF NONLINEAR SCHRODINGER-EQUATION WITH CRITICAL EXPONENT AND CRITICAL MASS

We consider the nonlinear Schrodinger equation with critical power (1) i partial derivative of u with respect to t = -DELTA-u - \u\4/(N)u, (1') u(0,.) = phi(.), where u : [0, T) x R(N) --> C and phi is-an-element-of H-1 and {phi;\x\phi is-an-element-of L2}. With this nonlinear term, the equation (1)-(1') has a conformal invariance. Thus one yields explicit "self-similar" solutions which have the following property: they have minimum L2 norm among blow-up solutions. In this paper, we first focus on uniqueness properties of these self-similar solutions in a certain class. We then look at the possible continuations of these solutions after the blow-up time.