A weak solvability to the steady Navier-Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions

0378946 - MÚ 2013 GB eng J - Článek v odborném periodiku
Muzereau, O. - Neustupa, Jiří - Penel, P.
A weak solvability to the steady Navier-Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions.
Applicable Analysis. Roč. 90, č. 1 (2011), s. 141-157. ISSN 0003-6811. E-ISSN 1563-504X
Klíčová slova: Navier-Stokes equations * compressible fluids * weak solution
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.744, rok: 2011
http://www.tandfonline.com/doi/abs/10.1080/00036811003738828

We prove the existence of a steady solution to the Navier–Stokes equations for barotropic compressible fluid in a bounded simply connected domain with the prescribed generalized impermeability conditions u · n = 0, curl u · n = 0 and curl 2 u · n = 0 on the boundary, we assume that the state law for the pressure has the form P(ρ) = ργ for . We prove several auxiliary lemmas, e.g. on solution of the Stokes problem with the generalized impermeability boundary conditions in W 2, p (Ω) or on the extension of the equation of continuity satisfied in the sense of distributions from ′(Ω) to ′(3) for velocity with the normal component on the boundary of Ω equal to zero.
Trvalý link: http://hdl.handle.net/11104/0210253