Optimal polynomial blow up range for critical wave maps
نویسندگان
چکیده
We prove that the critical Wave Maps equation with target S2 and origin R2+1 admits energy class blow up solutions of the form u(t ,r ) =Q(λ(t )r )+ε(t ,r ) where Q : R2 → S2 is the ground state harmonic map and λ(t) = t−1−ν for any ν > 0. This extends the work [17], where such solutions were constructed under the assumption ν> 2 . Also in the later chapter, we give the necessary remarks and key changes one needs to notice while the same problem is considered in a more general case while N is a surface of revolution. We are also able to extends the blow-up range in Carstea’s work [3] to ν> 0. In light of a result of Struwe [29], our results are optimal for polynomial blow up rates.
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