Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise

Leanne Dong

doi:10.3934/dcdsb.2020352

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2021, Volume 26, Issue 10: 5421-5448. Doi: 10.3934/dcdsb.2020352

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Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise

Leanne Dong^,

Gina Cody School of Engineering and Computer Science, 1455 De Maisonneuve Blvd., W. Montreal, QC H3G 1M8, Canada

Corresponding author: Leanne Dong
Corresponding author: Leanne Dong

Received: November 2019

Revised: June 2020

Early access: December 2020

Published: October 2021

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Abstract

In this paper we prove that the stochastic Navier-Stokes equations with stable Lévy noise generate a random dynamical systems. Then we prove the existence of random attractor for the Navier-Stokes equations on 2D spheres under stable Lévy noise (finite dimensional). We also deduce the existence of a Feller Markov Invariant Measure.

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Mathematics Subject Classification: Primary: 60H15, 35R60; Secondary: 37H10, 34F05.

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