Previous |  Up |  Next

Article

Keywords:
Navier-Stokes system; rough boundary; slip boundary condition
Summary:
The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.
References:
[1] Amirat, Y., Bresch, D., Lemoine, J., Simon, J.: Effect of rugosity on a flow governed by stationary Navier-Stokes equations. Q. Appl. Math. 59 (2001), 768-785. MR 1866556 | Zbl 1019.76014
[2] Bucur, D., Feireisl, E., Nečasová, Š.: On the asymptotic limit of flows past a ribbed boundary. J. Math. Fluid Mech. 10 (2008), 554-568. DOI 10.1007/s00021-007-0242-1 | MR 2461251 | Zbl 1189.35219
[3] Bucur, D., Feireisl, E., Nečasová, Š.: Boundary behavior of viscous fluids: Influence of wall roughness and friction-driven boundary conditions. Arch. Ration. Mech. Anal. 197 (2010), 117-138. DOI 10.1007/s00205-009-0268-z | MR 2646816 | Zbl 1273.76073
[4] Bucur, D., Feireisl, E., Nečasová, Š., Wolf, J.: On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries. J. Differ. Equations 244 (2008), 2890-2908. DOI 10.1016/j.jde.2008.02.040 | MR 2418180 | Zbl 1143.35080
[5] Bulíček, M., Málek, J., Rajagopal, K. R.: Navier's slip and evolutionary Navier-Stokes-like systems with pressure and shear-rate dependent viscosity. Indiana Univ. Math. J. 56 (2007), 51-85. DOI 10.1512/iumj.2007.56.2997 | MR 2305930 | Zbl 1129.35055
[6] Casado-Díaz, J., Fernández-Cara, E., Simon, J.: Why viscous fluids adhere to rugose walls: A mathematical explanation. J. Differ. Equations 189 (2003), 526-537. DOI 10.1016/S0022-0396(02)00115-8 | MR 1964478 | Zbl 1061.76014
[7] Jaeger, W., Mikelić, A.: On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Differ. Equations 170 (2001), 96-122. DOI 10.1006/jdeq.2000.3814 | MR 1813101 | Zbl 1009.76017
[8] Koch, H., Solonnikov, V. A.: $L_p$ estimates for a solution to the nonstationary Stokes equations. J. Math. Sci. 106 (2001), 3042-3072. DOI 10.1023/A:1011375706754 | MR 1906033 | Zbl 0987.35121
[9] Nitsche, J. A.: On Korn's second inequality. RAIRO, Anal. Numér. 15 (1981), 237-248. MR 0631678 | Zbl 0467.35019
[10] Sohr, H.: The Navier-Stokes Equations. An Elementary Functional Analytic Approach. Birkhäuser Basel (2001). MR 1928881 | Zbl 0983.35004
[11] Wolf, J.: Existence of weak solutions to the equations of non-stationary motion of non-Newtonian fluids with shear rate dependent viscosity. J. Math. Fluid Mech. 9 (2007), 104-138. DOI 10.1007/s00021-006-0219-5 | MR 2305828 | Zbl 1151.76426
Partner of
EuDML logo