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Steady compressible Oseen flow with slip boundary conditions

Tom 86 / 2009

Tomasz Piasecki Banach Center Publications 86 (2009), 247-264 MSC: 35Q10, 76N10. DOI: 10.4064/bc86-0-16

Streszczenie

We prove the existence of solution in the class $H^2(\Omega) \times H^1(\Omega)$ to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class $H^{5/2}$. The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary.

Autorzy

  • Tomasz PiaseckiMathematical Institute
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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