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.

Luigi C. Berselli. (2020). 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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