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On the Existence of Leray-Hopf Weak Solutions to the Navier-Stokes Equations
| Content Provider | MDPI |
|---|---|
| Author | Berselli, Luigi C. Spirito, Stefano |
| Copyright Year | 2021 |
| Description | We give a rather short and self-contained presentation of the global existence for Leray-Hopf weak solutions to the three dimensional incompressible Navier-Stokes equations, with constant density. We give a unified treatment in terms of the domains and the relative boundary conditions and in terms of the approximation methods. More precisely, we consider the case of the whole space, the flat torus, and the case of a general bounded domain with a smooth boundary (the latter supplemented with homogeneous Dirichlet conditions). We consider as approximation schemes the Leray approximation method, the Faedo-Galerkin method, the semi-discretization in time and the approximation by adding a Smagorinsky-Ladyžhenskaya term. We mainly focus on developing a unified treatment especially in the compactness argument needed to show that approximations converge to the weak solutions. |
| Starting Page | 42 |
| e-ISSN | 23115521 |
| DOI | 10.3390/fluids6010042 |
| Journal | Fluids |
| Issue Number | 1 |
| Volume Number | 6 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-01-13 |
| Access Restriction | Open |
| Subject Keyword | Fluids Mathematical Physics Navier-stokes Equations Leray-hopf Weak Solutions Existence |
| Content Type | Text |
| Resource Type | Article |
