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Peer-reviewedCC BY-NC-NDAnnals of Mathematics and Computer Science

3D Navier-Stokes Equation with Multivalued Friction

  • Simon ZONGO1
  • Bila Adolphe Kyelem2
  1. 1Laboratoire de Mathématiques, Informatique et Applications (L@MIA), Université Norbert ZONGO
  2. 2Département de Mathématiques et Informatique, Unité de Formation et de Recherche en Sciences et Technologies, Université Lédéa Bernard Ouédraogo, Burkina Faso
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Abstract

We prove the existence of weak solutions and their continuous dependence on the data for a three-dimensional incompressible Navier-Stokes system subject to multivalued friction boundary conditions, within a Hilbert space framework. Under suitable assumptions, a fixed point argument yields the existence of a solution to the associated perturbed stationary problem. Using nonlinear semigroup theory, we then establish the existence of a mild solution to the non-stationary problem and prove a contraction principle. Finally, by combining the Crandall-Liggett implicit discretization scheme with a priori estimates for the approximating mild solutions, we obtain weak solutions that depend continuously on the initial data.

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Cite

BibTeXRIS
BibTeX
@article{zongo2026navierstokes,
  title = {{3D Navier-Stokes Equation with Multivalued Friction}},
  author = {Simon ZONGO and Bila Adolphe Kyelem},
  journal = {Annals of Mathematics and Computer Science},
  year = {2026},
  month = jul,
  doi = {10.56947/amcs.v35.873},
  url = {https://doi.org/10.56947/amcs.v35.873},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - 3D Navier-Stokes Equation with Multivalued Friction
AU  - Simon ZONGO
AU  - Bila Adolphe Kyelem
PY  - 2026
DA  - 2026/07/21
JO  - Annals of Mathematics and Computer Science
DO  - 10.56947/amcs.v35.873
UR  - https://doi.org/10.56947/amcs.v35.873
AB  - We prove the existence of weak solutions and their continuous dependence on the data for a three-dimensional incompressible Navier-Stokes system subject to multivalued friction boundary conditions, within a Hilbert space framework. Under suitable assumptions, a fixed point argument yields the existence of a solution to the associated perturbed stationary problem. Using nonlinear semigroup theory, we then establish the existence of a mild solution to the non-stationary problem and prove a contraction principle. Finally, by combining the Crandall-Liggett implicit discretization scheme with a priori estimates for the approximating mild solutions, we obtain weak solutions that depend continuously on the initial data.
SN  - 2789-7206
ER  -