
Existence and stability of time periodic solution to the compressible NavierStokesKorteweg system on R^3Existence and stability of time periodic solution to the compressible NavierStokesKorteweg system on R^3 
"/Tsuda, Kazuyuki/"Tsuda, Kazuyuki
201520150430 , Faculty of Mathematics, Kyushu University
Description
The compressible NavierStokesKorteweg system is considered on R^3 when the external force is periodic in the time variable. The existence of a time periodic solution is proved for a sufficiently small external force by using the timeTmap related to the linearized problem around the motionless state with constant density and absolute temperature. The spectral properties of the timeTmap is investigated by a potential theoretic method and an energy method in some weighted spaces. The stability of the time periodic solution is proved for sufficiently small initial perturbations. It is also shown that the L^∞ norm of the perturbation decays as time goes to infinity.
FullText
http://catalog.lib.kyushuu.ac.jp/handle/2324/1525808/MI20155.pdf