Global existence for critical p = p: (T − t)-scaling

Global existence for critical p = p0: (T − t)-scaling Theorem 3.37 The Cauchy problem (41), (44) also has a global unique classical solution in the critical case

p = p0 = 1 + 2(2m−1)

N (m = 2l). (79)

Remark: on application of the Ck-scaling. For p = p0 in (69), μk → 0, but νk ≡ 1, so that, passing to the limit k → ∞, for the limit function wk(s) → w(s), we obtain the KSE in IRN × (−∞, 0) without the unstable diffusion-like term:

ws = −(−Δ)mw +B1|w|p, where |w(s)| ≤ 1, ‖w(s)‖2 ≤ C, supy |w(y, 0)| = 1.