\(L^2\)-decay of solutions to the Navier-Stokes system with Navier-type boundary conditions. (English) Zbl 1486.35323
Summary: We study in this paper the \(L^2\)-decay to the solutions of the Navier-Stokes system with Navier-type boundary conditions in a domain \(\Omega\) not necessarily simply connected. Since under this condition the Stokes operator has a non-trivial kernel we consider the solution lying in the orthogonal of that kernel. We also compare the decay rate of a weak solution to the Navier-Stokes problem with the solution to the linear problem emanating from the same initial data.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35D30 | Weak solutions to PDEs |
| 35D35 | Strong solutions to PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
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