Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

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We prove the semi-global controllability and stabilization of the

(1+1)-

dimensional wave maps equation with spatial domain 𝕊1 and target

𝕊k

. First we show that damping stabilizes the system when the energy is strictly below the threshold

2π

, where ha ...

For compact, isometrically embedded Riemannian manifolds N -> R-L, we introduce a fourth-order version of the wave maps equation. By energy estimates, we prove an a priori estimate for smooth local solutions in the energy subcritical dimension n = 1, 2. Th ...

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Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

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