A Morawetz type energy estimate for wave equation in $\mathbb{R}^2$ and application to elastic waves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914104320458752 |
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| author | Lai, Ningan Yin, Silu Zhou, Yi |
| author_facet | Lai, Ningan Yin, Silu Zhou, Yi |
| contents | In this paper, we introduce a modified scaling Morawetz multiplier, which produces a weighted Morawetz type energy (non-negative) estimate for the inhomogeneous wave equation in $\mathbb{R}^2$. With this estimate in hand, an alternative proof of global existence for the Cauchy problem of quasilinear wave equation with small and compactly supported data is given. What is more, such weighted Morawetz type energy estimate also works for certain wave system with multiple speeds, which can be used to prove global existence of some admissible harmonic elastic wave system in $\mathbb{R}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Morawetz type energy estimate for wave equation in $\mathbb{R}^2$ and application to elastic waves Lai, Ningan Yin, Silu Zhou, Yi Analysis of PDEs In this paper, we introduce a modified scaling Morawetz multiplier, which produces a weighted Morawetz type energy (non-negative) estimate for the inhomogeneous wave equation in $\mathbb{R}^2$. With this estimate in hand, an alternative proof of global existence for the Cauchy problem of quasilinear wave equation with small and compactly supported data is given. What is more, such weighted Morawetz type energy estimate also works for certain wave system with multiple speeds, which can be used to prove global existence of some admissible harmonic elastic wave system in $\mathbb{R}^2$. |
| title | A Morawetz type energy estimate for wave equation in $\mathbb{R}^2$ and application to elastic waves |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.17180 |