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Volume 19, Issue 4
Concerning Time-periodic Solutions of the Navier-Stokes Equations in Cylindrical Domains Under Navier Boundary Conditions

H. Beirão da Veiga

J. Part. Diff. Eq., 19 (2006), pp. 369-376.

Published online: 2006-11

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  • Abstract

The problem of the existence of time-periodic flows in infinite cylindrical pipes in correspondence to any given, time-periodic, total flux, was solved only quite recently in [1]. In this last reference we solved the above problem for flows under the non-slip boundary condition as a corollary of a more general result. Here we want to show that the abstract theorem proved in [1] applies as well to the solutions of the well known slip (or Navier) boundary condition (1.7) or to the mixed boundary condition (1.14). Actually, the argument applies for solutions of many other boundary value problems. This paper is a continuation of reference [1], to which the reader is referred for some notation and results.

  • Keywords

Flows in pipes time-periodic poiseuille slip boundary conditions

  • AMS Subject Headings

35Q30 35Q60 76D03.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-19-369, author = {H. Beirão da Veiga}, title = {Concerning Time-periodic Solutions of the Navier-Stokes Equations in Cylindrical Domains Under Navier Boundary Conditions}, journal = {Journal of Partial Differential Equations}, year = {2006}, volume = {19}, number = {4}, pages = {369--376}, abstract = {

The problem of the existence of time-periodic flows in infinite cylindrical pipes in correspondence to any given, time-periodic, total flux, was solved only quite recently in [1]. In this last reference we solved the above problem for flows under the non-slip boundary condition as a corollary of a more general result. Here we want to show that the abstract theorem proved in [1] applies as well to the solutions of the well known slip (or Navier) boundary condition (1.7) or to the mixed boundary condition (1.14). Actually, the argument applies for solutions of many other boundary value problems. This paper is a continuation of reference [1], to which the reader is referred for some notation and results.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5339.html} }
TY - JOUR T1 - Concerning Time-periodic Solutions of the Navier-Stokes Equations in Cylindrical Domains Under Navier Boundary Conditions AU - H. Beirão da Veiga JO - Journal of Partial Differential Equations VL - 4 SP - 369 EP - 376 PY - 2006 DA - 2006/11 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5339.html KW - Flows in pipes KW - time-periodic poiseuille KW - slip boundary conditions AB -

The problem of the existence of time-periodic flows in infinite cylindrical pipes in correspondence to any given, time-periodic, total flux, was solved only quite recently in [1]. In this last reference we solved the above problem for flows under the non-slip boundary condition as a corollary of a more general result. Here we want to show that the abstract theorem proved in [1] applies as well to the solutions of the well known slip (or Navier) boundary condition (1.7) or to the mixed boundary condition (1.14). Actually, the argument applies for solutions of many other boundary value problems. This paper is a continuation of reference [1], to which the reader is referred for some notation and results.

H. Beirão da Veiga. (2006). Concerning Time-periodic Solutions of the Navier-Stokes Equations in Cylindrical Domains Under Navier Boundary Conditions. Journal of Partial Differential Equations. 19 (4). 369-376. doi:
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