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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.11507 |
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| _version_ | 1866911672973656064 |
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| author | Marsden, Katie Rousset, Frédéric Schratz, Katharina |
| author_facet | Marsden, Katie Rousset, Frédéric Schratz, Katharina |
| contents | We prove convergence of a filtered Lie splitting scheme for the wave maps equation with low regularity initial data in dimension 3. The convergence analysis is performed in discrete Bourgain spaces, as has proved fruitful for the low regularity analysis of the equation in the continuous setting. An important difficulty here is that the analysis of wave maps at low regularity requires the use of the null structure of the system, this structure thus has to be preserved at the discrete level to get an effective stable low regularity scheme. Since the null structure involves time derivatives, the scheme has to be designed carefully. The presence of time derivatives in the nonlinearity then constitutes the most significant source of numerical error. Nonetheless, we are able to prove convergence of the scheme for all subcritical initial data in $H^s$, $s>d/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A splitting scheme for the wave maps equation at low regularity Marsden, Katie Rousset, Frédéric Schratz, Katharina Numerical Analysis 65M12, 35L05 We prove convergence of a filtered Lie splitting scheme for the wave maps equation with low regularity initial data in dimension 3. The convergence analysis is performed in discrete Bourgain spaces, as has proved fruitful for the low regularity analysis of the equation in the continuous setting. An important difficulty here is that the analysis of wave maps at low regularity requires the use of the null structure of the system, this structure thus has to be preserved at the discrete level to get an effective stable low regularity scheme. Since the null structure involves time derivatives, the scheme has to be designed carefully. The presence of time derivatives in the nonlinearity then constitutes the most significant source of numerical error. Nonetheless, we are able to prove convergence of the scheme for all subcritical initial data in $H^s$, $s>d/2$. |
| title | A splitting scheme for the wave maps equation at low regularity |
| topic | Numerical Analysis 65M12, 35L05 |
| url | https://arxiv.org/abs/2605.11507 |