A diversion to blow-up for n > 0

By using the same computations as above, we can prove the following blow-up result for the original equation (1):

Theorem 1.9 (Blow-up) Suppose that n > 0 in (166). Let

Φ(0) = 12 ∫ Ω |v0|

n+2 n+1 dx > 0 and

E(0) = − ∫ Ω |D˜mv0|2 dx+

∫ Ω v20 dx > 0.