The low mach number limit of global solutions to the full compressible Navier-Stokes system in critical Besov spaces with large initial data
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908858714161152 |
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| author | Li, Sai |
| author_facet | Li, Sai |
| contents | We are concerned with global existence of regular solutions to full compressible Navier-Stokes equations and their asymptotic behavior when the Mach number is sufficiently small. We establish global existence in critical Besov spaces for arbitrary large initial date provided that the divergence-free component of initial velocity and the difference between initial temperature and density generate a global regular solution to incompressible Boussinesq systems. Moreover, we rigorously justify the convergence to the incompressible model as the Mach number tends to zero. The proof relies on a fine-grained analysis of the high-middle-low frequencies of density, velocity and temperature. Our result can be seen as an improvement on Danchin and He [Math. Ann., 366 (2016), no. 3-4, pp. 1365-1402], including the extension from small initial data to large initial data and new convergence results which hold at the level of critical regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The low mach number limit of global solutions to the full compressible Navier-Stokes system in critical Besov spaces with large initial data Li, Sai Analysis of PDEs We are concerned with global existence of regular solutions to full compressible Navier-Stokes equations and their asymptotic behavior when the Mach number is sufficiently small. We establish global existence in critical Besov spaces for arbitrary large initial date provided that the divergence-free component of initial velocity and the difference between initial temperature and density generate a global regular solution to incompressible Boussinesq systems. Moreover, we rigorously justify the convergence to the incompressible model as the Mach number tends to zero. The proof relies on a fine-grained analysis of the high-middle-low frequencies of density, velocity and temperature. Our result can be seen as an improvement on Danchin and He [Math. Ann., 366 (2016), no. 3-4, pp. 1365-1402], including the extension from small initial data to large initial data and new convergence results which hold at the level of critical regularity. |
| title | The low mach number limit of global solutions to the full compressible Navier-Stokes system in critical Besov spaces with large initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.00900 |