Publikation:

Electro-rheological fluids under random influences : martingale and strong solutions

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2019

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Breit, Dominic

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URI (zitierfähiger Link)
http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1rwiucjmoky0a1
DOI (zitierfähiger Link)
https://doi.org/10.1007/s40072-019-00138-6
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CC BY 4.0

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Open Access Hybrid

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Mathematik und Statistik: Publikationen
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Stochastics and Partial Differential Equations: Analysis and Computations. Springer. 2019, 7(4), pp. 699-745. ISSN 2194-0401. eISSN 2194-041X. Available under: doi: 10.1007/s40072-019-00138-6

Zusammenfassung

We study generalised Navier–Stokes equations governing the motion of an electro-rheological fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii) a forcing term in the momentum equation represented by a multiplicative white noise and (iii) a random character of the variable exponent p=p(ω,t,x) (as a result of a random electric field). We show the existence of a weak martingale solution provided the variable exponent satisfies p≥p−>3n/n+2 (p−>1 in two dimensions). Under additional assumptions we obtain also stochastically strong solutions.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Electro-rheological fluids, Stochastic Navier–Stokes equations, Martingale solution, Pathwise solution

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ISO 690BREIT, Dominic, Franz GMEINEDER, 2019. Electro-rheological fluids under random influences : martingale and strong solutions. In: Stochastics and Partial Differential Equations: Analysis and Computations. Springer. 2019, 7(4), pp. 699-745. ISSN 2194-0401. eISSN 2194-041X. Available under: doi: 10.1007/s40072-019-00138-6
BibTex
@article{Breit2019-12Elect-53931,
  year={2019},
  doi={10.1007/s40072-019-00138-6},
  title={Electro-rheological fluids under random influences : martingale and strong solutions},
  number={4},
  volume={7},
  issn={2194-0401},
  journal={Stochastics and Partial Differential Equations: Analysis and Computations},
  pages={699--745},
  author={Breit, Dominic and Gmeineder, Franz}
}
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