Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth
Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth
复制标题
DOI：
10.1142/s0218202519500209
复制
发表时间：
2019-06-15
影响因子：
3.5
通讯作者：
Prazak, Dalibor
中科院分区：
文献类型：
--
作者：
Bulicek, Miroslav;Kaplicky, Petr;Prazak, Dalibor
本文研究了三维非牛顿流体在齐次Dirichlet边界条件下的流动。在Cauchy应力张量的自然单调性、单调性和增长性条件下，建立了方程解关于时间变量的正则性.因此，我们可以使用这些更好的信息来证明解的唯一性，只要初始数据对于所有幂律指数p >= 11/5都足够好。这样的结果是可用于p >= 12/5，因此，该文件填补了差距，并扩展的唯一性结果的整个范围的p的能量等式成立。
We deal with flows of non-Newtonian fluids in three-dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by a power index p >= 11/5, we establish regularity properties of a solution with respect to time variable. Consequently, we can use this better information for showing the uniqueness of the solution provided that the initial data are good enough for all power-law indices p >= 11/5. Such a result was available for p >= 12/5 and therefore the paper fills the gap and extends the uniqueness result to the whole range of p's for which the energy equality holds.