Time periodic problem for the compressible Navier–Stokes equation on ℝ<sup>2</sup> with antisymmetry

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  • Time periodic problem for the compressible Navier-Stokes equation on ℝ² with antisymmetry
  • Time periodic problem for the compressible Navier–Stokes equation on $\mathbb{R}^2$ with antisymmetry

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<p>The compressible Navier–Stokes 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 time-𝑇-map associated with the linearized problem around the motionless state with constant density. In some weighted 𝐿∞ and Sobolev spaces the spectral properties of the time-𝑇-map are 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 time-independent external force with antisymmetry condition on ℝ2.</p>

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