$H^2$-regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition
| Autor: | Fukao, Takeshi, Kashiwabara, Takahito |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | $H^2$-spatial regularity of stationary and non-stationary problems for Bingham fluids formulated with the pseudo-stress tensor is discussed. The problem is mathematically described by an elliptic or parabolic variational inequality of the second kind, to which weak solvability in the Sobolev space $H^1$ is well known. However, higher regularity up to the boundary in a bounded smooth domain seems to remain open. This paper indeed shows such $H^2$-regularity if the problems are supplemented with the so-called perfect slip boundary condition. For the stationary Bingham-Stokes problem, the key of the proof lies in a priori estimates for a regularized problem avoiding investigation of higher pressure regularity, which seems difficult to get in the presence of a singular diffusion term. The $H^2$-regularity for the stationary case is then directly applied to establish strong solvability of the non-stationary Bingham-Navier-Stokes problem, based on discretization in time and on the truncation of the nonlinear convection term. Comment: 21 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|