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<p>In this paper, we investigate a nonstationary Oseen-Navier-Stokes system for incompressible fluids under leak and slip boundary conditions, along with state constraints. The weak form of the system leads to a class of evolutionary quasi-variational hemivariational inequalities with nonhomogeneous initial conditions. By demonstrating the weak compactness of the solution set to the inequality problem, we establish the weak compactness of the solution set for the constrained nonstationary incompressible Oseen-Navier-Stokes system with mixed boundary value conditions. We then examine an optimal control problem associated with the system, which is motivated by important applications such as artificial heart models. General existence and compactness results for the optimal control problem are established.</p>

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Constrained nonstationary incompressible Oseen-Navier-Stokes system with leak and slip boundary conditions: existence and optimal control

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Guangkun Yang,
  • Zijia Peng,
  • Yu Zhang

摘要

In this paper, we investigate a nonstationary Oseen-Navier-Stokes system for incompressible fluids under leak and slip boundary conditions, along with state constraints. The weak form of the system leads to a class of evolutionary quasi-variational hemivariational inequalities with nonhomogeneous initial conditions. By demonstrating the weak compactness of the solution set to the inequality problem, we establish the weak compactness of the solution set for the constrained nonstationary incompressible Oseen-Navier-Stokes system with mixed boundary value conditions. We then examine an optimal control problem associated with the system, which is motivated by important applications such as artificial heart models. General existence and compactness results for the optimal control problem are established.