Abstract
In this paper, we study the vanishing dissipation limit problem for the full Navier–Stokes–Fourier equations with non-slip boundary condition in a smooth bounded domain \(\Omega \subseteq \mathbb {R}^{3}\). By using Kato’s idea (Math Sci Res Inst Publ 2:85–98, 1984) of constructing an artificial boundary layer, we obtain a sufficient condition for the convergence of the solution of the full Navier–Stokes–Fourier equations to the solution of the compressible Euler equations in the energy space \(L^{2}(\Omega )\) uniformly in time.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Chen, S.: Initial boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary. Front. Math. China 2, 87–102 (2007)
Feireisl, E., Novotný, A.: Singular Limits in Thermodynamical of Viscous Fluids. Birkhäuser-Verlag, Basel (2009)
Feireisl, E., Novotný, A.: Weak–strong uniqueness property for the full Navier–Stokes–Fourier system. Arch. Ration. Mech. Anal. 204, 683–706 (2012)
Feireisl, E.: Vanishing dissipation limit for the Navier–Stokes–Fourier system. arXiv:1506.02251
Kato, T.: Remarks on zero viscosity limit for nonstationary Navier–Stokes flows with boundary. Seminar on nonlinear partial differential equations. Math. Sci. Res. Inst. Publ. 2, 85–98 (1984)
Kawashima, S., Yanagisawa, T., Shizuta, Y.: Mixed problems for quasi-linear symmetric hyperbolic systems. Proc. Jpn. Acad. 63A, 243–246 (1987)
Lopes Filho, M.C., Nussenzveig Lopes, H.J., Titi, E.S., Zang, A.: Convergence of the 2D Euler-\(\alpha \) to Euler equations in the Dirichlet case: indifference to boundary layers. Phys. D 292–293, 51–61 (2015)
Lopes Filho, M.C., Nussenzveig Lopes, H.J., Titi, E.S., Zang, A.: Approximation of 2D Euler equations by the second-grade fluid equations with Dirichlet boundary condition. J. Math. Fluid Mech. 17, 327–340 (2015)
Maekawa, Y., Mazzucato, A.: The inviscid limit and boundary layers for Navier–Stokes flows. arXiv:1610.05372
Prandtl, L.: Über Flüssigkeitsbewegungen bei sehr kleiner Reibung, in “Verh. Int. Math. Kongr., Heidelberg 1904”, Teubner 1905, pp. 484–494
Sueur, F.: On the inviscid limit for the compressible Navier–Stokes system in an impermeable bounded domain. J. Math. Fluid Mech. 1, 163–178 (2014)
Wang, X.M.: A Kato type theorem on zero viscosity limit of Navier–Stokes flow. Indiana Univ. Math. J. (Special Issue) 50, 223–241 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by G.P. Galdi
Rights and permissions
About this article
Cite this article
Wang, YG., Zhu, SY. On the Vanishing Dissipation Limit for the Full Navier–Stokes–Fourier System with Non-slip Condition. J. Math. Fluid Mech. 20, 393–419 (2018). https://doi.org/10.1007/s00021-017-0326-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00021-017-0326-5