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On finite-dimensional attractor to 2D incompressible fluid with stress-diffusion

  • Dalibor Pražák
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Abstract

We consider incompressible visco-elastic rate-type fluid flow, with the Cauchy stress defined in terms of positive-definite symmetric tensor B. The tensor B obeys an evolution equation, combining Oldroyd-B and Giesekus model, and, crucially, a diffusion term. Restricting ourselves to the 2D periodic problem, we show existence of a finite-dimensional global attractor. We also estimate its dimension explicitely in terms of the equation parameters.

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Cite

BibTeXRIS
BibTeX
@misc{prazak2026finitedimensional,
  title = {{On finite-dimensional attractor to 2D incompressible fluid with stress-diffusion}},
  author = {Dalibor Pražák},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29290},
  eprint = {2610.29290},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29290},
}
RIS
TY  - UNPB
TI  - On finite-dimensional attractor to 2D incompressible fluid with stress-diffusion
AU  - Dalibor Pražák
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29290
UR  - https://arxiv.org/abs/2610.29290
AB  - We consider incompressible visco-elastic rate-type fluid flow, with the Cauchy stress defined in terms of positive-definite symmetric tensor B. The tensor B obeys an evolution equation, combining Oldroyd-B and Giesekus model, and, crucially, a diffusion term. Restricting ourselves to the 2D periodic problem, we show existence of a finite-dimensional global attractor. We also estimate its dimension explicitely in terms of the equation parameters.
ER  -