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- W2244522020 abstract "In this paper we consider the equation for equivariant wave maps from $mathbb {R}^{3+1}$ to $mathbb {S}^3$ and we prove global in forward time existence of certain $C^infty$-smooth solutions which have infinite critical Sobolev norm $dot {H}^{frac {3}{2}}(mathbb {R}^3)times dot {H}^{frac {1}{2}}(mathbb {R}^3)$. Our construction provides solutions which can moreover satisfy the additional size condition $|u(0, cdot )|_{L^infty (|x|geq 1)}>M$ for arbitrarily chosen $M>0$. These solutions are also stable under suitable perturbations. Our method, strongly inspired by work of Krieger and Schlag, is based on a perturbative approach around suitably constructed approximate selfâsimilar solutions." @default.
- W2244522020 created "2016-06-24" @default.
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- W2244522020 date "2016-06-20" @default.
- W2244522020 modified "2023-10-16" @default.
- W2244522020 title "A class of large global solutions for the wave-map equation" @default.
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- W2244522020 doi "https://doi.org/10.1090/tran/6805" @default.
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