$\mathbb{L}^p-$solutions of the stochastic Navier-Stokes equations subject to Lévy noise with $\mathbb{L}^m(\mathbb{R}^m)$ initial data

Manil T. Mohan; Sivaguru S. Sritharan

doi:10.3934/eect.2017021

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2017, Volume 6, Issue 3: 409-425. Doi: 10.3934/eect.2017021

This issue Previous Article Null controllability for parabolic equations with dynamic boundary conditions Next Article Sensitivity analysis in set-valued optimization under strictly minimal efficiency

$\mathbb{L}^p-$solutions of the stochastic Navier-Stokes equations subject to Lévy noise with $\mathbb{L}^m(\mathbb{R}^m)$ initial data

Manil T. Mohan^1, and
Sivaguru S. Sritharan^2, ,

1.
Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, OH 45433, USA
2.
Office of the Provost & Vice Chancellor, Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, OH 45433, USA

*Corresponding author: Sivaguru S. Sritharan
*Corresponding author: Sivaguru S. Sritharan

Received: February 2017

Revised: March 2017

Published: October 2017

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Abstract

In this work, we establish the local solvability of the stochastic Navier-Stokes equations in $\mathbb{R}^m$ , $m≥ 2$ , perturbed by Lévy noise in $\mathbb L^p-$ spaces for $p∈[m,∞)$ with an $\mathbb L^m(\mathbb{R}^m)-$ valued initial data.

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Mathematics Subject Classification: Primary: 76D06; Secondary: 35Q30, 76D03, 47D03.

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