Geodesic
On the Homogenization Principle in a Time-Periodic Problem for the Navier--Stokes Equations with Rapidly Oscillating Mass Force
Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 764-777

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We study the behavior of the set of time-periodic solutions of the three-dimensional system of Navier–Stokes equations in a bounded domain as the frequency of the oscillations of the right-hand side tends to infinity. It is established that the set of periodic solutions tends to the solution set of the homogenized stationary equation.
Keywords: system of Navier–Stokes equations, homogenization principle, Hilbert space, periodic solution, strong solution. 
@article{MZM_2016_99_5_a9,
     author = {V. L. Khatskevich},
     title = {On the {Homogenization} {Principle} in a {Time-Periodic} {Problem} for the {Navier--Stokes} {Equations} with {Rapidly} {Oscillating} {Mass} {Force}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {764--777},
     publisher = {mathdoc},
     volume = {99},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a9/}
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V. L. Khatskevich. On the Homogenization Principle in a Time-Periodic Problem for the Navier--Stokes Equations with Rapidly Oscillating Mass Force. Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 764-777. http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a9/