Lp-solutions for stochastic Navier–Stokes equations with jump noise

Jiahui Zhu; Zdzislaw Brzezniak; Wei Liu

doi:10.1016/j.spl.2019.108563

L^p-solutions for stochastic Navier–Stokes equations with jump noise

Jiahui Zhu, Zdzislaw Brzezniak, Wei Liu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the existence and uniqueness of solutions of 2D Stochastic Navier–Stokes equation with space irregular jump noise for initial data in certain Sobolev spaces of negative order. Comparing with the Galerkin approximation method, the main advantage of this work is to use an L^p-setting to obtain the solution under much weaker assumptions on the noise and the initial condition.

Original language	English
Article number	108563
Number of pages	9
Journal	Statistics and Probability Letters
Volume	155
Early online date	1 Aug 2019
DOIs	https://doi.org/10.1016/j.spl.2019.108563
Publication status	Published - 1 Dec 2019

Keywords

L-theory
Poisson random measure
Stochastic Navier–Stokes equation

Access to Document

10.1016/j.spl.2019.108563

Cite this

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abstract = "We study the existence and uniqueness of solutions of 2D Stochastic Navier–Stokes equation with space irregular jump noise for initial data in certain Sobolev spaces of negative order. Comparing with the Galerkin approximation method, the main advantage of this work is to use an Lp-setting to obtain the solution under much weaker assumptions on the noise and the initial condition.",

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AU - Brzezniak, Zdzislaw

AU - Liu, Wei

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AB - We study the existence and uniqueness of solutions of 2D Stochastic Navier–Stokes equation with space irregular jump noise for initial data in certain Sobolev spaces of negative order. Comparing with the Galerkin approximation method, the main advantage of this work is to use an Lp-setting to obtain the solution under much weaker assumptions on the noise and the initial condition.

KW - L-theory

KW - Poisson random measure

KW - Stochastic Navier–Stokes equation

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