Singularity formation for the two-dimensional harmonic map flow into $$S^2$$
نویسندگان
چکیده
منابع مشابه
Singularity Formation for the Two-dimensional Harmonic Map Flow into S
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S2, ut = ∆u+ |∇u|u in Ω× (0, T ) u = φ on ∂Ω× (0, T ) u(·, 0) = u0 in Ω, where Ω is a bounded, smooth domain in R2, u : Ω×(0, T ) → S2, u0 : Ω̄ → S2 is smooth, and φ = u0 ∣∣ ∂Ω . Given any points q1, . . . , qk in the domain, we find initial and boundary data so that the solution blows-up precisely ...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2019
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-019-00908-y