The global strong solution to compressible system with fractional viscous term
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914855326318592 |
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| author | Liu, Mengqian Niu, Lei Wu, Zhigang |
| author_facet | Liu, Mengqian Niu, Lei Wu, Zhigang |
| contents | In this paper, we study the Cauchy problem to the 3D fractional compressible isentropic generalized Navier-Stokes equations for viscous compressible fluid with one Levy diffusion process. We obtain the existence and uniqueness of global strong solution for small initial data by providing several commutators via the Littlewood-Paley theory. Moreover, we derive $L^2$-decay rate for the highest derivative of the strong solution without decay loss by using a cancellation of a low-medium-frequency quantity. Our results improve the results provided in [J. Differential Equations 377(2023): 369-417]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11877 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The global strong solution to compressible system with fractional viscous term Liu, Mengqian Niu, Lei Wu, Zhigang Analysis of PDEs 35A09, 35B40, 35Q35 In this paper, we study the Cauchy problem to the 3D fractional compressible isentropic generalized Navier-Stokes equations for viscous compressible fluid with one Levy diffusion process. We obtain the existence and uniqueness of global strong solution for small initial data by providing several commutators via the Littlewood-Paley theory. Moreover, we derive $L^2$-decay rate for the highest derivative of the strong solution without decay loss by using a cancellation of a low-medium-frequency quantity. Our results improve the results provided in [J. Differential Equations 377(2023): 369-417]. |
| title | The global strong solution to compressible system with fractional viscous term |
| topic | Analysis of PDEs 35A09, 35B40, 35Q35 |
| url | https://arxiv.org/abs/2311.11877 |