A construction of blow up solutions for co-rotational wave maps
Carstea, Catalin I.
Original · EN
The existence of co-rotational finite time blow up solutions to the wave map problem from R²⁺¹ into N, where N is a surface of revolution with metric dρ²+g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(λ(t)t)+R(t,r), where Q is a time independent solution of the co-rotational wave map equation -utt+urr+r⁻¹uᵣ=r⁻²g(u)g'(u), λ(t)=t⁻¹⁻ν, ν>1/2 is arbitrary, and R is a term whose local energy goes to zero as t goes to 0.
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