
Time periodic problem for the compressible NavierStokes equation on R^2 with antisymmetryTime periodic problem for the compressible NavierStokes equation on R^2 with antisymmetry 
"/Tsuda, Kazuyuki/"Tsuda, Kazuyuki
2016720160506 , Faculty of Mathematics, Kyushu University
Description
The compressible NavierStokes equation is considered on the two dimensional whole space when the external force is periodic in the time variable. The existence of a time periodic solution is proved for sufficiently small time periodic external force with antisymmetry condition. The proof is based on using the timeTmap associated with the linearized problem around the motionless state with constant density. In some weighted L^∞ and Sobolev spaces the spectral properties of the timeTmap is investigated by a potential theoretic method and an energy method. The existence of a stationary solution to the stationary problem is also shown for sufficiently small timeindependent external force with antisymmetry condition on R^2.
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