2月4日(金)
16:00--17:30 CRESTセミナー　(合同棟508B・C)
吉田　伸生 氏（京都大学大学院理学研究科）
Stochastic Shear Thickening Fluids: Strong Convergence of the Galerkin Approximation and the Energy Equality.
[アブストラクト]
We consider a SPDE (stochastic partial differential equation) 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: $p \in [1 +{d \over 2}, {2d \over d-2})$, where $d$ is the dimension of the space. We prove that the Galerkin scheme approximates the the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.