Rauch条件下半变分发展Navier-斯托克斯方程的弱解与最优控制
Weak solutions and optimal control of hemivariational evolutionary Navier-Stokes equations under Rauch condition
摘要：
本文考虑了非滑移边界条件下的演化Navier-斯托克斯方程，其中动压与速度法向分量之间存在Clarke次微分关系。在Rauch条件下，我们利用Galerkin逼近方法和弱预紧性准则来保证问题收敛到期望解。此外，与这样的方程组的控制问题进行了研究的帮助下，相对于外力的稳定性结果。本文最后给出了由Z. Naniewicz，即定向生长条件，被认为是和所有的结果重新检查。
英文摘要：
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.
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