Fujita-Kato solution for the 3D compressible pressureless Navier-Stokes equations with discontinuous and large-variation density
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915444223377408 |
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| author | Xu, Xiaojie Wang. Jiahong Wu. Fuyi |
| author_facet | Xu, Xiaojie Wang. Jiahong Wu. Fuyi |
| contents | This paper mainly focuses on the Cauchy problem to the 3D compressible pressureless Navier-Stokes equations arising from models of collective behavior, which can be derived by taking the high Mach number limit of the classical compressible Navier-Stokes system. We construct the global-in-time existence and uniqueness of the so-called Fujita-Kato solution to the system, provided that the initial density $ρ_0$ is discontinuous, large-variation and the initial velocity $u_0$ is in a critical functional framework. Our method relies on some time weighted estimates and the Lagrangian approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fujita-Kato solution for the 3D compressible pressureless Navier-Stokes equations with discontinuous and large-variation density Xu, Xiaojie Wang. Jiahong Wu. Fuyi Analysis of PDEs This paper mainly focuses on the Cauchy problem to the 3D compressible pressureless Navier-Stokes equations arising from models of collective behavior, which can be derived by taking the high Mach number limit of the classical compressible Navier-Stokes system. We construct the global-in-time existence and uniqueness of the so-called Fujita-Kato solution to the system, provided that the initial density $ρ_0$ is discontinuous, large-variation and the initial velocity $u_0$ is in a critical functional framework. Our method relies on some time weighted estimates and the Lagrangian approach. |
| title | Fujita-Kato solution for the 3D compressible pressureless Navier-Stokes equations with discontinuous and large-variation density |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.09764 |