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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18425 |
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| _version_ | 1866909269197062144 |
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| author | Jiang, Yiming Ren, Jingchuang Wei, Yawei |
| author_facet | Jiang, Yiming Ren, Jingchuang Wei, Yawei |
| contents | This paper concerns the Cauchy problems for the nonlinear Rayleigh-Stokes equation and the corresponding system with time-fractional derivative of order $α\in(0,1)$, which can be used to simulate the anomalous diffusion in viscoelastic fluids. It is shown that there exists the critical Fujita exponent which separates systematic blow-up of the solutions from possible global existence, and the critical exponent is independent of the parameter $α$. Different from the general scaling argument for parabolic problems, the main ingredients of our proof are suitable decay estimates of the solution operator and the construction of the test function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fujita phenomena in nonlinear fractional Rayleigh-Stokes equations Jiang, Yiming Ren, Jingchuang Wei, Yawei Analysis of PDEs This paper concerns the Cauchy problems for the nonlinear Rayleigh-Stokes equation and the corresponding system with time-fractional derivative of order $α\in(0,1)$, which can be used to simulate the anomalous diffusion in viscoelastic fluids. It is shown that there exists the critical Fujita exponent which separates systematic blow-up of the solutions from possible global existence, and the critical exponent is independent of the parameter $α$. Different from the general scaling argument for parabolic problems, the main ingredients of our proof are suitable decay estimates of the solution operator and the construction of the test function. |
| title | Fujita phenomena in nonlinear fractional Rayleigh-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.18425 |