JournalsaihpcVol. 36, No. 5pp. 1237–1280

The vanishing viscosity limit for some symmetric flows

  • Gung-Min Gie

    Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY 40292, USA

  • James P. Kelliher

    Department of Mathematics, University of California, Riverside, 900 University Ave., Riverside, CA 92521, USA

  • Milton C. Lopes Filho

    Instituto de Matematica, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21941-909, Rio de Janeiro, RJ, Brazil

  • Anna L. Mazzucato

    Department of Mathematics, Penn State University, University Park, PA 16802, USA

  • Helena J. Nussenzveig Lopes

    Instituto de Matematica, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21941-909, Rio de Janeiro, RJ, Brazil
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Abstract

The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit boundary layer correctors, which approximate the difference between the Navier–Stokes and the Euler solutions. Using properties of these correctors, we establish convergence of the Navier–Stokes solution to the Euler solution as viscosity vanishes with optimal rates of convergence. In addition, we investigate vorticity production on the boundary in the limit of vanishing viscosity. Our work significantly extends prior work in the literature.

Cite this article

Gung-Min Gie, James P. Kelliher, Milton C. Lopes Filho, Anna L. Mazzucato, Helena J. Nussenzveig Lopes, The vanishing viscosity limit for some symmetric flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 5, pp. 1237–1280

DOI 10.1016/J.ANIHPC.2018.11.006