Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773885 | Journal of Differential Equations | 2017 | 35 Pages |
Abstract
We discuss the time periodic problem to the incompressible Navier-Stokes equations on the whole space Rn, nâ¥3, with the external forces of non-divergence form. Firstly, we consider the existence of time periodic solutions in BC(R;Ln,â(Rn)) assuming the smallness of external forces in BC(R;L1(R3)) and BC(R;Ln3,â(Rn)) in the case nâ¥4. Next, we show that the mild solution above becomes a strong solution in the topology of Ln,â(Rn) with a natural condition of the external force, derived from the strong solvability of the inhomogeneous Stokes equations in Ln,â(Rn). For this aim, we re-construct a strong solvability of an abstract evolution equation where the associated semigroup is not strongly continuous at t=0.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Takahiro Okabe, Yohei Tsutsui,