High viscosity limit for the multi-dimensional compressible Navier-Stokes equations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914397868261376 |
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| author | Danchin, Raphaël |
| author_facet | Danchin, Raphaël |
| contents | We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant viscosity coefficients, we establish that, after diffusive rescaling, the density tends to satisfy a transport equation with nonlinear damping which is globally well-posed, even for large data. Similar results are proved for variable viscosity coefficients. In this latter case, the damping term in the limit equation of the density is nonlocal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High viscosity limit for the multi-dimensional compressible Navier-Stokes equations Danchin, Raphaël Analysis of PDEs We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant viscosity coefficients, we establish that, after diffusive rescaling, the density tends to satisfy a transport equation with nonlinear damping which is globally well-posed, even for large data. Similar results are proved for variable viscosity coefficients. In this latter case, the damping term in the limit equation of the density is nonlocal. |
| title | High viscosity limit for the multi-dimensional compressible Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.15209 |