标题： 基于压力边界条件的Navier-Stokes方程最优控制 显示英文标题

标题： Optimal Control of the Navier-Stokes equations via Pressure Boundary Conditions

摘要： 在本工作中，我们研究了一个受非定常纳维-斯托克斯方程约束的最优控制问题，其中控制通过非齐次诺伊曼/无条件边界条件进入。 尽管这些边界条件下纳维-斯托克斯方程在长时间和/或大数据情况下可能不适定，但我们通过选择适当的跟踪类型项获得了最优控制问题的适定性。 为了讨论最优控制、状态和伴随状态的正则性，我们提出了关于带有混合非齐次边界条件的斯托克斯问题解的$L^2(I;H^2(\Omega))$正则性的新结果。 显示英文摘要

摘要： In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these boundary conditions not being well-posed for large times and/or data, we obtain wellposedness of the optimal control problem by choosing a proper tracking type term. In order to discuss the regularity of the optimal control, state and adjoint state, we present new results on $L^2(I;H^2(\Omega))$ regularity of solutions to a Stokes problem with mixed inhomogeneous boundary conditions.