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

Maria Rosaria Lancia; Paola Vernole

doi:10.3934/dcdss.2020088

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2020, Volume 13, Issue 5: 1553-1565. Doi: 10.3934/dcdss.2020088

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

Maria Rosaria Lancia^, and
Paola Vernole

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
^* Corresponding author: Maria Rosaria Lancia

Received: January 2018

Revised: June 2018

Published: March 2020

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q35, 47D06, 47D06, 28A80.

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Figure 1. Koch snowflake

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Figure 2. The prefractal $ F_h $ at the step $ h = 2 $ and $ h = 5 $

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Figure 3. Surface $ S_3 $

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