Asymptotic limit of the compressible Navier–Stokes system on domains with rough boundaries

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Abstract
In this paper, we study the asymptotic behavior of solutions to the compressible Navier–Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the full-slip boundary conditions, we show that in the asymptotic limit the fluid sticks completely to the boundary, provided the oscillations are non-degenerate, meaning not oriented in a single direction.
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Funding Information
  • Grantová Agentura České Republiky (GA22-01591S)
  • Czech Academy of Sciences (Praemium Academiae of S.N.)
  • Akademie Věd České Republiky (Praemium Academiae of S.N.)
  • JUNTA/ FEDER (US-1381261)
  • Institute of Mathematics of the Czech Academy of Sciences

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