论文标题
弱解决方案和最佳控制半传向进化的Navier-Stokes方程在劳奇条件下
Weak solutions and optimal control of hemivariational evolutionary Navier-Stokes equations under Rauch condition
论文作者
论文摘要
在本文中，我们考虑了受不态度边界条件的进化纳维尔 - 斯托克斯方程，以及动态压力与速度的正常成分之间的CLARKE细分关系。在劳奇条件下，我们使用盖金近似方法和弱编译标准来确保收敛到所需溶液。此外，还研究了与此类方程系统相关的控制问题，在外部力量方面的稳定性结果的帮助下。在本文的最后，考虑了Z. naniewicz引起的更一般的条件，即定向生长条件，并重新检查所有结果。
In this paper we consider evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under Rauch condition, we use the Galerkin approximation method and a weak precompactness criteria to ensure the convergence to a desired solution. Moreover a control problem associated with such system of equations is studied with the help of a stability result with respect to the external forces. In the end of this paper, a more general condition due to Z. Naniewicz, namely the directional growth condition, is considered and all the results are reexamined.
