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Volume 15, Issue 4-5
Weak Solutions Constructed by Semi-Discretization are Suitable: The Case of Slip Boundary Conditions

Luigi C. Berselli

Int. J. Numer. Anal. Mod., 15 (2018), pp. 479-491.

Published online: 2018-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We consider the initial boundary value problem for the three dimensional Navier-Stokes equations with Navier-type slip boundary conditions. After having properly formulated the problem, we prove that weak solutions constructed by approximating the time-derivative by backward finite differences (with Euler schemes) are suitable. The main novelty is the proof of the local energy inequality in the case of a weak solution constructed by time discretization. Moreover, the problem is analyzed with boundary conditions which are of particular interest in view of applications to turbulent flows.

  • Keywords

Navier-Stokes equations, Euler scheme, local energy inequality, slip boundary conditions.

  • AMS Subject Headings

35Q30, 35A35, 65M20, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

luigi.carlo.berselli@unipi.it (Luigi C. Berselli)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-479, author = {Berselli , Luigi C.}, title = {Weak Solutions Constructed by Semi-Discretization are Suitable: The Case of Slip Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {479--491}, abstract = {

We consider the initial boundary value problem for the three dimensional Navier-Stokes equations with Navier-type slip boundary conditions. After having properly formulated the problem, we prove that weak solutions constructed by approximating the time-derivative by backward finite differences (with Euler schemes) are suitable. The main novelty is the proof of the local energy inequality in the case of a weak solution constructed by time discretization. Moreover, the problem is analyzed with boundary conditions which are of particular interest in view of applications to turbulent flows.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12526.html} }
TY - JOUR T1 - Weak Solutions Constructed by Semi-Discretization are Suitable: The Case of Slip Boundary Conditions AU - Berselli , Luigi C. JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 479 EP - 491 PY - 2018 DA - 2018/04 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12526.html KW - Navier-Stokes equations, Euler scheme, local energy inequality, slip boundary conditions. AB -

We consider the initial boundary value problem for the three dimensional Navier-Stokes equations with Navier-type slip boundary conditions. After having properly formulated the problem, we prove that weak solutions constructed by approximating the time-derivative by backward finite differences (with Euler schemes) are suitable. The main novelty is the proof of the local energy inequality in the case of a weak solution constructed by time discretization. Moreover, the problem is analyzed with boundary conditions which are of particular interest in view of applications to turbulent flows.

Berselli , Luigi C.. (2018). Weak Solutions Constructed by Semi-Discretization are Suitable: The Case of Slip Boundary Conditions. International Journal of Numerical Analysis and Modeling. 15 (4-5). 479-491. doi:
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