Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915415751393280 |
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| author | Sasaki, Takiko Shao, Kerun Takamura, Hiroyuki |
| author_facet | Sasaki, Takiko Shao, Kerun Takamura, Hiroyuki |
| contents | This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial derivatives of the unknown function. Such a proof is so-called "slicing method", which may help us to extend the result for various equations and systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations Sasaki, Takiko Shao, Kerun Takamura, Hiroyuki Analysis of PDEs primary 35L71, secondary 35B44 This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial derivatives of the unknown function. Such a proof is so-called "slicing method", which may help us to extend the result for various equations and systems. |
| title | Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations |
| topic | Analysis of PDEs primary 35L71, secondary 35B44 |
| url | https://arxiv.org/abs/2504.19107 |