STOCHASTIC SHEAR THICKENING FLUIDS: STRONG CONVERGENCE OF THE GALERKIN APPROXIMATION AND THE ENERGY EQUALITY

• 成果类型: Article
• 署名作者: Yoshida, Nobuo
• 署名单位: Kyoto University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP794
• 发表日期: 2012
• 页码: 1215-1242
• 关键词: navier-stokes equations

摘要

We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here, the extra stress tensor of the fluid is given by a polynomial of degree p - 1 of the rate of strain tensor, while the colored noise is considered as a random force. We focus on the shear thickening case, more precisely, on the case p is an element of [1 + d/2, 2d/d-2), where d is the dimension of the space. We prove that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.