Vanishing viscosity limit for incompressible flow inside a rotating circle

M. C. Lopes Filho; A. L. Mazzucato; H. J. Nussenzveig Lopes

doi:10.1016/j.physd.2008.03.009

Vanishing viscosity limit for incompressible flow inside a rotating circle

M. C. Lopes Filho, A. L. Mazzucato, H. J. Nussenzveig Lopes

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52 Scopus citations

Abstract

In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary has finite total variation, then the Navier-Stokes solutions converge strongly in L² to the corresponding stationary solution of the Euler equations when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation.

Original language	English (US)
Pages (from-to)	1324-1333
Number of pages	10
Journal	Physica D: Nonlinear Phenomena
Volume	237
Issue number	10-12
DOIs	https://doi.org/10.1016/j.physd.2008.03.009
State	Published - Jul 15 2008

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2008.03.009

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title = "Vanishing viscosity limit for incompressible flow inside a rotating circle",

abstract = "In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary has finite total variation, then the Navier-Stokes solutions converge strongly in L2 to the corresponding stationary solution of the Euler equations when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation.",

author = "{Lopes Filho}, {M. C.} and Mazzucato, {A. L.} and {Nussenzveig Lopes}, {H. J.}",

note = "Funding Information: The authors wish to thank Aloisio Neves and Victor Nistor for helpful discussions. A. L. M. would like to thank the hospitality of IMECC-UNICAMP, where most of this research was done. This work was supported in part by FAPESP Grant # 06/00252-6. The first author was partially supported by CNPq grant # 302.102/2004-3. The second author was partially supported by NSF grant DMS 0405803. The third author was partially supported by CNPq grant # 302.214/2004-6.",

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doi = "10.1016/j.physd.2008.03.009",

language = "English (US)",

volume = "237",

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T1 - Vanishing viscosity limit for incompressible flow inside a rotating circle

AU - Lopes Filho, M. C.

AU - Mazzucato, A. L.

AU - Nussenzveig Lopes, H. J.

N1 - Funding Information: The authors wish to thank Aloisio Neves and Victor Nistor for helpful discussions. A. L. M. would like to thank the hospitality of IMECC-UNICAMP, where most of this research was done. This work was supported in part by FAPESP Grant # 06/00252-6. The first author was partially supported by CNPq grant # 302.102/2004-3. The second author was partially supported by NSF grant DMS 0405803. The third author was partially supported by CNPq grant # 302.214/2004-6.

PY - 2008/7/15

Y1 - 2008/7/15

N2 - In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary has finite total variation, then the Navier-Stokes solutions converge strongly in L2 to the corresponding stationary solution of the Euler equations when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation.

AB - In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary has finite total variation, then the Navier-Stokes solutions converge strongly in L2 to the corresponding stationary solution of the Euler equations when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation.

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DO - 10.1016/j.physd.2008.03.009

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EP - 1333

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 10-12

ER -

Vanishing viscosity limit for incompressible flow inside a rotating circle

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