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arXiv · 2102.12881

Global results for a Cauchy problem related to biharmonic wave maps

Tobias Schmid
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Abstract

We prove global existence of a derivative bi-harmonic wave equation with a non-generic quadratic nonlinearity and small initial data in the scaling critical space $\dot{B}^{2,1}_{\frac{d}{2}}(\mathbb{R}^d) \times \dot{B}^{2,1}_{\frac{d}{2}-2}(\mathbb{R}^d)$ for $ d \geq 3 $. Since the solution persists higher regularity of the initial data, we obtain a small data global regularity result for the biharmonic wave maps equation for a certain class of target manifolds including the sphere.

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Tobias Schmid. 2021-02-25. Global results for a Cauchy problem related to biharmonic wave maps. https://doi.org/10.2140/paa.2024.6.657

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