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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2102.12881 |
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| _version_ | 1866916418160689152 |
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| author | Schmid, Tobias |
| author_facet | Schmid, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_12881 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Global results for a Cauchy problem related to biharmonic wave maps Schmid, Tobias Analysis of PDEs 35A01 (Primary), 35G50 (Secondary) 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. |
| title | Global results for a Cauchy problem related to biharmonic wave maps |
| topic | Analysis of PDEs 35A01 (Primary), 35G50 (Secondary) |
| url | https://arxiv.org/abs/2102.12881 |