TY - JOUR

T1 - The vanishing viscosity limit for some symmetric flows

AU - Gie, Gung Min

AU - Kelliher, James P.

AU - Lopes Filho, Milton C.

AU - Mazzucato, Anna L.

AU - Nussenzveig Lopes, Helena J.

N1 - Funding Information:
The authors acknowledge the support in this work of various grants and institutions, as follows. G.-M. Gie: the Research – RI Grant 51018, Office of the Executive Vice President for Research and Innovation, University of Louisville; G.-M. Gie and J. Kelliher: US National Science Foundation (NSF) grants DMS-1009545 and DMS-1212141; M. Lopes Filho: CNPq grants #200434/2011-0 and #306886/2014-6; A. Mazzucato: NSF grants DMS-1009713, DMS-1009714, DMS-1312727, and DMS-1615457; H. Nussenzveig Lopes: CAPES grant BEX 6649/10-6, CNPq grant #307918/2014-9, and FAPERJ grant #E-26/202.950/2015. J. Kelliher, M. Lopes Filho, and H. Nussenzveig Lopes: the National Institute for Pure and Applied Mathematics (IMPA) in Rio de Janeiro in residence Spring 2014; M. Lopes Filho and H. Nussenzveig Lopes: the Dept. of Mathematics at the University of California, Riverside in residence Fall 2011; A. Mazzucato: the Institute for Pure and Applied Mathematics (IPAM) at UCLA in residence Fall 2014 (IPAM receives major support from the NSF under Grant No. DMS-1440415); the second through fifth authors: the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI, in residence Spring 2017 (ICERM receives major support from NSF under Grant No. DMS-1439786). The authors thank Gregory Eyink for pointing out a useful reference.
Funding Information:
The authors acknowledge the support in this work of various grants and institutions, as follows. G.-M. Gie: the Research – RI Grant 51018 , Office of the Executive Vice President for Research and Innovation, University of Louisville ; G.-M. Gie and J. Kelliher: US National Science Foundation (NSF) grants DMS-1009545 and DMS-1212141 ; M. Lopes Filho: CNPq grants # 200434/2011-0 and # 306886/2014-6 ; A. Mazzucato: NSF grants DMS-1009713 , DMS-1009714 , DMS-1312727 , and DMS-1615457 ; H. Nussenzveig Lopes: CAPES grant BEX 6649/10-6 , CNPq grant # 307918/2014-9 , and FAPERJ grant # E-26/202.950/2015 . J. Kelliher, M. Lopes Filho, and H. Nussenzveig Lopes: the National Institute for Pure and Applied Mathematics (IMPA) in Rio de Janeiro in residence Spring 2014; M. Lopes Filho and H. Nussenzveig Lopes: the Dept. of Mathematics at the University of California, Riverside in residence Fall 2011; A. Mazzucato: the Institute for Pure and Applied Mathematics (IPAM) at UCLA in residence Fall 2014 (IPAM receives major support from the NSF under Grant No. DMS-1440415 ); the second through fifth authors: the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI, in residence Spring 2017 (ICERM receives major support from NSF under Grant No. DMS-1439786 ). The authors thank Gregory Eyink for pointing out a useful reference.
Funding Information:
The authors acknowledge the support in this work of various grants and institutions, as follows. G.-M. Gie: the Research ? RI Grant 51018, Office of the Executive Vice President for Research and Innovation, University of Louisville; G.-M. Gie and J. Kelliher: US National Science Foundation (NSF) grants DMS-1009545 and DMS-1212141; M. Lopes Filho: CNPq grants #200434/2011-0 and #306886/2014-6; A. Mazzucato: NSF grants DMS-1009713, DMS-1009714, DMS-1312727, and DMS-1615457; H. Nussenzveig Lopes: CAPES grant BEX 6649/10-6, CNPq grant #307918/2014-9, and FAPERJ grant #E-26/202.950/2015. J. Kelliher, M. Lopes Filho, and H. Nussenzveig Lopes: the National Institute for Pure and Applied Mathematics (IMPA) in Rio de Janeiro in residence Spring 2014; M. Lopes Filho and H. Nussenzveig Lopes: the Dept. of Mathematics at the University of California, Riverside in residence Fall 2011; A. Mazzucato: the Institute for Pure and Applied Mathematics (IPAM) at UCLA in residence Fall 2014 (IPAM receives major support from the NSF under Grant No. DMS-1440415); the second through fifth authors: the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI, in residence Spring 2017 (ICERM receives major support from NSF under Grant No. DMS-1439786). The authors thank Gregory Eyink for pointing out a useful reference.
Publisher Copyright:
© 2018 Elsevier Masson SAS

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85057989387&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057989387&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2018.11.006

DO - 10.1016/j.anihpc.2018.11.006

M3 - Article

AN - SCOPUS:85057989387

VL - 36

SP - 1237

EP - 1280

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 5

ER -