Remark on random attractor for a two dimensional incompressible non-Newtonian fluid withmultiplicative noise
Remark on random attractor for a two dimensional incompressible non-Newtonian fluid withmultiplicative noise
复制标题
DOI：
10.4310/cms.2012.v10.n3.a5
复制
发表时间：
2012
影响因子：
1
通讯作者：
B. Guo;Chunxiao Guo
中科院分区：
文献类型：
--
作者：
B. Guo;Chunxiao Guo
其中ωj（t），1 ≤ j≤m是相互独立的双边Wiener过程，bj ∈R，1≤ j≤m是已知的.未知矢量函数u表示流体的速度，g是外部体力矢量，标量函数π表示压力，τij（e（u））是对称应力张量。存在许多流体材料-例如液体泡沫和聚合物流体（诸如水包油、血液等）-其粘性应力张量由形式τij（e（u））=2μ0（μ 1 + μ 2）表示。|e（u）|）p−2 2 eij（u）−2μ1 eij（u），> 0，i，j= 1，2，（1.5）
where ◦ denotes the Stratonovich sense in the stochastic term, ωj(t),1≤ j≤m are mutually independent two-sided Wiener processes, and bj ∈R,1≤ j≤m are given. The unknown vector function u denotes the velocity of the fluids, g is the external body force vector, the scalar function π represents the pressure, and τij(e(u)) is a symmetric stress tensor. There are many fluid materials — for example liquid foams and polymeric fluids such as oil in water, blood, etc. — whose viscous stress tensors are represented by the form τij(e(u))=2μ0(ǫ+ |e(u)| ) p−2 2 eij(u)−2μ1∆eij(u), ǫ> 0, i,j=1,2, (1.5)