On Kato’s conditions for the inviscid limit of the two-dimensional stochastic Navier-Stokes equation-Reference-Cited by-同舟云学术

On Kato’s conditions for the inviscid limit of the two-dimensional stochastic Navier-Stokes equation

Published:2024-08-01 Issue:8 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Wang Ya-guang¹^ORCID,Zhao Meng²^ORCID

Affiliation:

1. School of Mathematical Sciences, Center for Applied Mathematics, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University 1 , 200240 Shanghai, China

2. School of Mathematical Sciences, Shanghai Jiao Tong University 2 , 200240 Shanghai, China

Abstract

We study the asymptotic behavior of solutions of the two-dimensional stochastic Navier-Stokes (SNS) equation with no-slip boundary condition in the small viscosity limit. Several equivalent dissipation conditions of the Kato type are derived to ensure that the convergence from the SNS equation to the corresponding stochastic Euler equation holds in the energy space. We do not assume any smallness on the noise of the SNS equation.

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0175063/20112100/081507_1_5.0175063.pdf

Reference33 articles.

1. Mathematics and turbulence: Where do we stand?;J. Turbul.,2013

2. Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II. Construction of the Navier-Stokes solution;Commun. Math. Phys.,1998

3. Zero-viscosity limit of the Navier-Stokes equations in the analytic setting;Arch. Ration. Mech. Anal.,2017

4. The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary;Arch. Ration. Mech. Anal.,2020

5. On the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half-plane;Commun. Pure Appl. Math.,2014