# American Institute of Mathematical Sciences

## The Stokes problem in fractal domains: Asymptotic behaviour of the solutions

 Dipartimento di Scienze di Base e Applicate per I'Ingegneria, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy

* Corresponding author: Maria Rosaria Lancia

Received  January 2018 Revised  June 2018 Published  June 2019

We study a Stokes problem in a three dimensional fractal domain of Koch type and in the corresponding prefractal approximating domains. We prove that the prefractal solutions do converge to the limit fractal one in a suitable sense. Namely the approximating velocity vector fields as well as the approximating associated pressures converge to the limit fractal ones respectively.

Citation: Maria Rosaria Lancia, Paola Vernole. The Stokes problem in fractal domains: Asymptotic behaviour of the solutions. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020088
##### References:

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##### References:
Koch snowflake
The prefractal $F_h$ at the step $h = 2$ and $h = 5$
Surface $S_3$
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