Suitable weak solutions to the 3D Navier–Stokes equations are constructed with the Voigt approximation
| Autor: | Luigi C. Berselli, Stefano Spirito |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Initial boundary value problem
Navier–Stokes equations Navier–Stokes–Voigt model Suitable weak solution Analysis suitable solutions Navier-Stokes Mathematics::Analysis of PDEs Slip (materials science) 01 natural sciences Voigt models Dirichlet distribution Physics::Fluid Dynamics symbols.namesake Mathematics - Analysis of PDEs FOS: Mathematics Applied mathematics Boundary value problem Navier stokes 0101 mathematics Mathematics Energy inequality Applied Mathematics 010102 general mathematics Vorticity 010101 applied mathematics symbols Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Differential Equations. 262:3285-3316 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2016.11.027 |
| Popis: | In this paper we consider the Navier–Stokes equations supplemented with either the Dirichlet or vorticity-based Navier slip boundary conditions. We prove that weak solutions obtained as limits of solutions of the Navier–Stokes–Voigt model satisfy the local energy inequality, and we also prove certain regularity results for the pressure. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions through a Fourier–Galerkin finite-dimensional approximation in the space variables. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect