Blow-up and sharp lifespan estimates to the weakly coupled system of structurally damped wave equations with critical nonlinearities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917388776112128 |
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| author | Tang, Trung Loc Dao, Tuan Anh Cung, The Anh |
| author_facet | Tang, Trung Loc Dao, Tuan Anh Cung, The Anh |
| contents | In this paper, we would like to study the weakly coupled system of semilinear structurally damped wave equations with moduli of continuity in nonlinear terms whose powers belong to the critical curve in the $p-q$ plane. Our main purpose is to find a sharp condition for these moduli of continuity by investigating the global (in time) existence of small data Sobolev solutions and the blow-up result for solutions in finite time as well. Furthermore, when the blow-up phenomenon occurs, we are going to achieve the sharp lifespan estimates for the local (in time) Sobolev solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blow-up and sharp lifespan estimates to the weakly coupled system of structurally damped wave equations with critical nonlinearities Tang, Trung Loc Dao, Tuan Anh Cung, The Anh Analysis of PDEs 26A15, 35A01, 35L52 In this paper, we would like to study the weakly coupled system of semilinear structurally damped wave equations with moduli of continuity in nonlinear terms whose powers belong to the critical curve in the $p-q$ plane. Our main purpose is to find a sharp condition for these moduli of continuity by investigating the global (in time) existence of small data Sobolev solutions and the blow-up result for solutions in finite time as well. Furthermore, when the blow-up phenomenon occurs, we are going to achieve the sharp lifespan estimates for the local (in time) Sobolev solution. |
| title | Blow-up and sharp lifespan estimates to the weakly coupled system of structurally damped wave equations with critical nonlinearities |
| topic | Analysis of PDEs 26A15, 35A01, 35L52 |
| url | https://arxiv.org/abs/2603.12673 |