Blow up of the critical norm for some radial L super critical non linear Schrödinger equations
نویسندگان
چکیده
We consider the nonlinear Schrödinger equation iut = −∆u−|u|p−1u in dimension N ≥ 3 in the L super critical range N+3 N−1 ≤ p < N+2 N−2 . The corresponding scaling invariant space is Ḣc with 1 2 ≤ sc < 1 and this covers the physically relevant case N = 3, p = 3. The existence of finite time blow up solutions is known. Let u(t) ∈ Ḣc ∩ Ḣ be a radially symmetric blow up solution which blows up at 0 < T < +∞, we prove that the scaling invariant Ḣc norm also blows up with a lower bound: |u(t)|Ḣsc ≥ |log(T − t)|N,p as t → T.
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