Smooth type II blow up solutions to the four dimensional energy critical wave equation
نویسندگان
چکیده
We exhibit C∞ type II blow up solutions to the focusing energy critical wave equation in dimension N = 4. These solutions admit near blow up time a decomposiiton u(t, x) = 1 λ N−2 2 (t) (Q+ ε(t))( x λ(t) ) with ‖ε(t), ∂tε(t)‖Ḣ1×L2 ≪ 1 where Q is the extremizing profile of the Sobolev embedding Ḣ → L∗ , and a blow up speed λ(t) = (T − t)e− √ |log(T−t)|(1+o(1)) as t → T.
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