---

The Navier-Stokes equations with damping describe the flow with the resistance to motion. From a mathematical viewpoint, the equations can be viewed as a modification of the Navier-Stokes equations with the regularizing term. This monograph concerns the initial-boundary value problems for the Navier-Stokes equations with damping and the Bousssinesq system with damping in a bounded set, respectively. First, the existences of strong solutions of both problems for a certain range of parameters are proved. Second, for the Navier-Stokes equations with damping, the uniqueness of weak solutions which are limitations of a sequence of the approximation strong solutions is proved under the same conditions on parameters. Finally, some conditions on parameters to guarantee the existence and globally asymptotic stability for the time-periodic solutions of both problems are found, respectively.

---

Yongho Kim Studied Mathematics at University of Science. Senior Researcher at the University of Science, Pyongyang, DPR Korea.

---