A revisit via slicing method on a quadratic semilinear wave equation in two space dimensions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917471688065024 |
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| author | Kato, Masakazu Takamura, Hiroyuki Wakasa, Kyouhei |
| author_facet | Kato, Masakazu Takamura, Hiroyuki Wakasa, Kyouhei |
| contents | In this paper, we are focusing on proofs of a blow-up result for a quadratic semilinear wave equation in two space dimensions. There is a logarithmic loss in estimating the lifespan of a classical solution if the 0th moment of the initial speed does not vanish. This result is already known with almost sharp constants. But in order to have a direct application to the numerical analysis, we show a simple proof by iteration argument for a point-wise estimate of the solution with a slicing technique. Such a research direction can be found in the case of critical nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07290 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A revisit via slicing method on a quadratic semilinear wave equation in two space dimensions Kato, Masakazu Takamura, Hiroyuki Wakasa, Kyouhei Analysis of PDEs primary 35L71, secondary 35B44 In this paper, we are focusing on proofs of a blow-up result for a quadratic semilinear wave equation in two space dimensions. There is a logarithmic loss in estimating the lifespan of a classical solution if the 0th moment of the initial speed does not vanish. This result is already known with almost sharp constants. But in order to have a direct application to the numerical analysis, we show a simple proof by iteration argument for a point-wise estimate of the solution with a slicing technique. Such a research direction can be found in the case of critical nonlinearity. |
| title | A revisit via slicing method on a quadratic semilinear wave equation in two space dimensions |
| topic | Analysis of PDEs primary 35L71, secondary 35B44 |
| url | https://arxiv.org/abs/2605.07290 |