Abstract
We show that solutions of the Navier–Stokes–Fourier system describing the motion of a general viscous, compressible, and heat conducting fluid stabilize to an equilibrium provided the fluid is driven by highly oscillating forces with polynomial growth in time. This means that though the force we consider is unbounded, thanks to the rapid oscillations the solution will still converge to the homogeneous static state as time approaches infinity.
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Acknowledgments
The work of P.B. was partially supported by the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503, and by NSF through Grant DMS-0807347. The work of E.F. was supported by Grant 201/09/0917 of GA ČR as a part of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503. The work of D.P. was supported by Grant 201/09/0917 of GA ČR and by the Grant MSM 0021620839 of the Czech Ministry of Education.
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Bella, P., Feireisl, E. & Pražák, D. Long Time Behavior and Stabilization to Equilibria of Solutions to the Navier–Stokes–Fourier System Driven by Highly Oscillating Unbounded External Forces. J Dyn Diff Equat 25, 257–268 (2013). https://doi.org/10.1007/s10884-013-9299-0
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DOI: https://doi.org/10.1007/s10884-013-9299-0